SlideShare a Scribd company logo
1 of 19
Download to read offline
solution:
A=
1
1
0
4
3
1
2
0
5
Finding the determinant of the matrix ?
det A = -3
The determinant of A is non-zero, hence the inverse matrix A-1 exists. To find the inverse
matrix was calculated the minors and cofactors of the matrix ?
M1,1 =
3
1
0
5
=
15
C1,1 = (-1)1+1M1,1 =
15
M1,2 =
4
1
2
5
=
18
C1,2 = (-1)1+2M1,2 =
-18
M1,3 =
4
3
2
0
=
-6
C1,3 = (-1)1+3M1,3 =
-6
M2,1 =
1
0
0
5
=
5
C2,1 = (-1)2+1M2,1 =
-5
M2,2 =
1
0
2
5
=
5
C2,2 = (-1)2+2M2,2 =
5
M2,3 =
1
1
2
0
=
-2
C2,3 = (-1)2+3M2,3 =
2
M3,1 =
1
0
3
1
=
1
C3,1 = (-1)3+1M3,1 =
1
M3,2 =
1
0
4
1
=
1
C3,2 = (-1)3+2M3,2 =
-1
M3,3 =
1
1
4
3
=
-1
C3,3 = (-1)3+3M3,3 =
-1
Matrix of cofactors:
C =
15
-18
-6
-5
5
2
1
-1
-1
Transpose of cofactor matrix:
CT =
15
-5
1
-18
5
-1
-6
2
-1
Finding the inverse matrix.
A-1 =
CT
=
det A
-5
5/3
-1/3
6
-5/3
1/3
2
-2/3
1/3
B)
First, let's add the Identity Matrix to the right of our matrix
1
1
0
1
0
0
4
3
1
0
1
0
2
0
5
0
0
1
Now, let's do Gauss-Jordan Elimination on our new matrix...
Add (-4 * row1) to row2
1
1
0
1
0
0
0
-1
1
-4
1
0
2
0
5
0
0
1
Add (-2 * row1) to row3
1
1
0
1
0
0
0
-1
1
-4
1
0
0
-2
5
-2
0
1
Divide row2 by -1
1
1
0
1
0
0
0
1
-1
4
-1
0
0
-2
5
-2
0
1
Add (2 * row2) to row3
1
1
0
1
0
0
0
1
-1
4
-1
0
0
0
3
6
-2
1
Divide row3 by 3
1
1
0
1
0
0
0
1
-1
4
-1
0
0
0
1
2
-2/3
1/3
Add (1 * row3) to row2
1
1
0
1
0
0
0
1
0
6
-5/3
1/3
0
0
1
2
-2/3
1/3
Add (-1 * row2) to row1
1
0
0
-5
5/3
-1/3
0
1
0
6
-5/3
1/3
0
0
1
2
-2/3
1/3
The inverse matrix can now be found in the right 3 columns of our reduced row echelon matrix
Here is the inverse matrix:
-5
5/3
-1/3
6
-5/3
1/3
2
-2/3
1/3
A=
1
1
0
4
3
1
2
0
5
Solution
solution:
A=
1
1
0
4
3
1
2
0
5
Finding the determinant of the matrix ?
det A = -3
The determinant of A is non-zero, hence the inverse matrix A-1 exists. To find the inverse
matrix was calculated the minors and cofactors of the matrix ?
M1,1 =
3
1
0
5
=
15
C1,1 = (-1)1+1M1,1 =
15
M1,2 =
4
1
2
5
=
18
C1,2 = (-1)1+2M1,2 =
-18
M1,3 =
4
3
2
0
=
-6
C1,3 = (-1)1+3M1,3 =
-6
M2,1 =
1
0
0
5
=
5
C2,1 = (-1)2+1M2,1 =
-5
M2,2 =
1
0
2
5
=
5
C2,2 = (-1)2+2M2,2 =
5
M2,3 =
1
1
2
0
=
-2
C2,3 = (-1)2+3M2,3 =
2
M3,1 =
1
0
3
1
=
1
C3,1 = (-1)3+1M3,1 =
1
M3,2 =
1
0
4
1
=
1
C3,2 = (-1)3+2M3,2 =
-1
M3,3 =
1
1
4
3
=
-1
C3,3 = (-1)3+3M3,3 =
-1
Matrix of cofactors:
C =
15
-18
-6
-5
5
2
1
-1
-1
Transpose of cofactor matrix:
CT =
15
-5
1
-18
5
-1
-6
2
-1
Finding the inverse matrix.
A-1 =
CT
=
det A
-5
5/3
-1/3
6
-5/3
1/3
2
-2/3
1/3
B)
First, let's add the Identity Matrix to the right of our matrix
1
1
0
1
0
0
4
3
1
0
1
0
2
0
5
0
0
1
Now, let's do Gauss-Jordan Elimination on our new matrix...
Add (-4 * row1) to row2
1
1
0
1
0
0
0
-1
1
-4
1
0
2
0
5
0
0
1
Add (-2 * row1) to row3
1
1
0
1
0
0
0
-1
1
-4
1
0
0
-2
5
-2
0
1
Divide row2 by -1
1
1
0
1
0
0
0
1
-1
4
-1
0
0
-2
5
-2
0
1
Add (2 * row2) to row3
1
1
0
1
0
0
0
1
-1
4
-1
0
0
0
3
6
-2
1
Divide row3 by 3
1
1
0
1
0
0
0
1
-1
4
-1
0
0
0
1
2
-2/3
1/3
Add (1 * row3) to row2
1
1
0
1
0
0
0
1
0
6
-5/3
1/3
0
0
1
2
-2/3
1/3
Add (-1 * row2) to row1
1
0
0
-5
5/3
-1/3
0
1
0
6
-5/3
1/3
0
0
1
2
-2/3
1/3
The inverse matrix can now be found in the right 3 columns of our reduced row echelon matrix
Here is the inverse matrix:
-5
5/3
-1/3
6
-5/3
1/3
2
-2/3
1/3
A=
1
1
0
4
3
1
2
0
5

More Related Content

Similar to solutionA=  1    1    0    4    3    1    2    0 .pdf

Jawapan matriks spM LATIH TUBI 2015
Jawapan matriks spM LATIH TUBI 2015Jawapan matriks spM LATIH TUBI 2015
Jawapan matriks spM LATIH TUBI 2015
aloysiusapat
 

Similar to solutionA=  1    1    0    4    3    1    2    0 .pdf (19)

5.3 geometric sequences and sums t
5.3 geometric sequences and sums t5.3 geometric sequences and sums t
5.3 geometric sequences and sums t
 
Jawapan matriks spM LATIH TUBI 2015
Jawapan matriks spM LATIH TUBI 2015Jawapan matriks spM LATIH TUBI 2015
Jawapan matriks spM LATIH TUBI 2015
 
chp-1-matrices-determinants1.ppt
chp-1-matrices-determinants1.pptchp-1-matrices-determinants1.ppt
chp-1-matrices-determinants1.ppt
 
APM.pdf
APM.pdfAPM.pdf
APM.pdf
 
1301 c1 january_2013_mark_scheme
1301 c1 january_2013_mark_scheme1301 c1 january_2013_mark_scheme
1301 c1 january_2013_mark_scheme
 
Chapter 03 matrices
Chapter 03 matricesChapter 03 matrices
Chapter 03 matrices
 
Matrix.pptx
Matrix.pptxMatrix.pptx
Matrix.pptx
 
chp-1-matrices-determinants1 (2).ppt
chp-1-matrices-determinants1 (2).pptchp-1-matrices-determinants1 (2).ppt
chp-1-matrices-determinants1 (2).ppt
 
Chapter001
Chapter001Chapter001
Chapter001
 
Business mathametics and statistics b.com ii semester (2)
Business mathametics and statistics b.com ii semester (2)Business mathametics and statistics b.com ii semester (2)
Business mathametics and statistics b.com ii semester (2)
 
Matrices
MatricesMatrices
Matrices
 
Determinants and matrices.ppt
Determinants and matrices.pptDeterminants and matrices.ppt
Determinants and matrices.ppt
 
TABREZ KHAN.ppt
TABREZ KHAN.pptTABREZ KHAN.ppt
TABREZ KHAN.ppt
 
Mathematics 1
Mathematics 1Mathematics 1
Mathematics 1
 
Nuevo formulario
Nuevo formularioNuevo formulario
Nuevo formulario
 
Nvo formulario
Nvo formularioNvo formulario
Nvo formulario
 
Introduction of determinant
Introduction of determinantIntroduction of determinant
Introduction of determinant
 
Calculus And Its Applications 10th Edition Bittinger Solutions Manual
Calculus And Its Applications 10th Edition Bittinger Solutions ManualCalculus And Its Applications 10th Edition Bittinger Solutions Manual
Calculus And Its Applications 10th Edition Bittinger Solutions Manual
 
Analisys of Selection Sort and Bubble Sort
Analisys of Selection Sort and Bubble SortAnalisys of Selection Sort and Bubble Sort
Analisys of Selection Sort and Bubble Sort
 

More from arakalamkah11

1. A bus is a bunch of wires used to connect multiple subsystems. Bu.pdf
1. A bus is a bunch of wires used to connect multiple subsystems. Bu.pdf1. A bus is a bunch of wires used to connect multiple subsystems. Bu.pdf
1. A bus is a bunch of wires used to connect multiple subsystems. Bu.pdf
arakalamkah11
 
1. E) The vapor pressure of a liquid.Increasing attractive intermo.pdf
1. E) The vapor pressure of a liquid.Increasing attractive intermo.pdf1. E) The vapor pressure of a liquid.Increasing attractive intermo.pdf
1. E) The vapor pressure of a liquid.Increasing attractive intermo.pdf
arakalamkah11
 
Light is a form of energy that can be released by.pdf
                     Light is a form of energy that can be released by.pdf                     Light is a form of energy that can be released by.pdf
Light is a form of energy that can be released by.pdf
arakalamkah11
 
1) Presence of jaws with paired fins in fish helps to feed them. Fin.pdf
1) Presence of jaws with paired fins in fish helps to feed them. Fin.pdf1) Presence of jaws with paired fins in fish helps to feed them. Fin.pdf
1) Presence of jaws with paired fins in fish helps to feed them. Fin.pdf
arakalamkah11
 
Youre looking for Ka, the dissociation constant.pdf
                     Youre looking for Ka, the dissociation constant.pdf                     Youre looking for Ka, the dissociation constant.pdf
Youre looking for Ka, the dissociation constant.pdf
arakalamkah11
 
remote operating system installationRemote Installation Services (.pdf
remote operating system installationRemote Installation Services (.pdfremote operating system installationRemote Installation Services (.pdf
remote operating system installationRemote Installation Services (.pdf
arakalamkah11
 
Title of this process is The Project Life Cycle (Phases)The pr.pdf
Title of this process is The Project Life Cycle (Phases)The pr.pdfTitle of this process is The Project Life Cycle (Phases)The pr.pdf
Title of this process is The Project Life Cycle (Phases)The pr.pdf
arakalamkah11
 
Q1). Gene therapy is an experimental approach to treat the disease b.pdf
Q1). Gene therapy is an experimental approach to treat the disease b.pdfQ1). Gene therapy is an experimental approach to treat the disease b.pdf
Q1). Gene therapy is an experimental approach to treat the disease b.pdf
arakalamkah11
 
package s3; Copy paste this Java Template and save it as Emer.pdf
package s3;  Copy paste this Java Template and save it as Emer.pdfpackage s3;  Copy paste this Java Template and save it as Emer.pdf
package s3; Copy paste this Java Template and save it as Emer.pdf
arakalamkah11
 
Our body is having two line defence system against pathogens.Pathoge.pdf
Our body is having two line defence system against pathogens.Pathoge.pdfOur body is having two line defence system against pathogens.Pathoge.pdf
Our body is having two line defence system against pathogens.Pathoge.pdf
arakalamkah11
 

More from arakalamkah11 (20)

Particulars $Amount Direct materials 64452 Direct Labour (1332.pdf
    Particulars $Amount   Direct materials 64452   Direct Labour (1332.pdf    Particulars $Amount   Direct materials 64452   Direct Labour (1332.pdf
Particulars $Amount Direct materials 64452 Direct Labour (1332.pdf
 
Decrease in inventory Source of cash $   440 Decrease in account.pdf
    Decrease in inventory Source of cash $   440   Decrease in account.pdf    Decrease in inventory Source of cash $   440   Decrease in account.pdf
Decrease in inventory Source of cash $   440 Decrease in account.pdf
 
Diamond is sp3 covalent. It makes for bonds to ne.pdf
                     Diamond is sp3 covalent. It makes for bonds to ne.pdf                     Diamond is sp3 covalent. It makes for bonds to ne.pdf
Diamond is sp3 covalent. It makes for bonds to ne.pdf
 
Too low. If you do not dry the sodium thiosulfate.pdf
                     Too low. If you do not dry the sodium thiosulfate.pdf                     Too low. If you do not dry the sodium thiosulfate.pdf
Too low. If you do not dry the sodium thiosulfate.pdf
 
1. A bus is a bunch of wires used to connect multiple subsystems. Bu.pdf
1. A bus is a bunch of wires used to connect multiple subsystems. Bu.pdf1. A bus is a bunch of wires used to connect multiple subsystems. Bu.pdf
1. A bus is a bunch of wires used to connect multiple subsystems. Bu.pdf
 
1. E) The vapor pressure of a liquid.Increasing attractive intermo.pdf
1. E) The vapor pressure of a liquid.Increasing attractive intermo.pdf1. E) The vapor pressure of a liquid.Increasing attractive intermo.pdf
1. E) The vapor pressure of a liquid.Increasing attractive intermo.pdf
 
Light is a form of energy that can be released by.pdf
                     Light is a form of energy that can be released by.pdf                     Light is a form of energy that can be released by.pdf
Light is a form of energy that can be released by.pdf
 
1) Presence of jaws with paired fins in fish helps to feed them. Fin.pdf
1) Presence of jaws with paired fins in fish helps to feed them. Fin.pdf1) Presence of jaws with paired fins in fish helps to feed them. Fin.pdf
1) Presence of jaws with paired fins in fish helps to feed them. Fin.pdf
 
Youre looking for Ka, the dissociation constant.pdf
                     Youre looking for Ka, the dissociation constant.pdf                     Youre looking for Ka, the dissociation constant.pdf
Youre looking for Ka, the dissociation constant.pdf
 
Okay so dipole-dipole interactions would occur be.pdf
                     Okay so dipole-dipole interactions would occur be.pdf                     Okay so dipole-dipole interactions would occur be.pdf
Okay so dipole-dipole interactions would occur be.pdf
 
remote operating system installationRemote Installation Services (.pdf
remote operating system installationRemote Installation Services (.pdfremote operating system installationRemote Installation Services (.pdf
remote operating system installationRemote Installation Services (.pdf
 
Title of this process is The Project Life Cycle (Phases)The pr.pdf
Title of this process is The Project Life Cycle (Phases)The pr.pdfTitle of this process is The Project Life Cycle (Phases)The pr.pdf
Title of this process is The Project Life Cycle (Phases)The pr.pdf
 
The answer is A) Pol II, with twelve subunits on its own, is capable.pdf
The answer is A) Pol II, with twelve subunits on its own, is capable.pdfThe answer is A) Pol II, with twelve subunits on its own, is capable.pdf
The answer is A) Pol II, with twelve subunits on its own, is capable.pdf
 
Q1). Gene therapy is an experimental approach to treat the disease b.pdf
Q1). Gene therapy is an experimental approach to treat the disease b.pdfQ1). Gene therapy is an experimental approach to treat the disease b.pdf
Q1). Gene therapy is an experimental approach to treat the disease b.pdf
 
Solution Three modes of DNA replication 1) Semi conservative.pdf
Solution Three modes of DNA replication 1) Semi conservative.pdfSolution Three modes of DNA replication 1) Semi conservative.pdf
Solution Three modes of DNA replication 1) Semi conservative.pdf
 
package s3; Copy paste this Java Template and save it as Emer.pdf
package s3;  Copy paste this Java Template and save it as Emer.pdfpackage s3;  Copy paste this Java Template and save it as Emer.pdf
package s3; Copy paste this Java Template and save it as Emer.pdf
 
Our body is having two line defence system against pathogens.Pathoge.pdf
Our body is having two line defence system against pathogens.Pathoge.pdfOur body is having two line defence system against pathogens.Pathoge.pdf
Our body is having two line defence system against pathogens.Pathoge.pdf
 
Once neurons are produced, they migrate and modify to form six layer.pdf
Once neurons are produced, they migrate and modify to form six layer.pdfOnce neurons are produced, they migrate and modify to form six layer.pdf
Once neurons are produced, they migrate and modify to form six layer.pdf
 
PDU is called Protocol Data Unit.It consists of user data and protoc.pdf
PDU is called Protocol Data Unit.It consists of user data and protoc.pdfPDU is called Protocol Data Unit.It consists of user data and protoc.pdf
PDU is called Protocol Data Unit.It consists of user data and protoc.pdf
 
1.A hole is the absence of an electron in a particular place in an a.pdf
1.A hole is the absence of an electron in a particular place in an a.pdf1.A hole is the absence of an electron in a particular place in an a.pdf
1.A hole is the absence of an electron in a particular place in an a.pdf
 

Recently uploaded

會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
中 央社
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
中 央社
 
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPSSpellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
AnaAcapella
 

Recently uploaded (20)

UChicago CMSC 23320 - The Best Commit Messages of 2024
UChicago CMSC 23320 - The Best Commit Messages of 2024UChicago CMSC 23320 - The Best Commit Messages of 2024
UChicago CMSC 23320 - The Best Commit Messages of 2024
 
An Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge AppAn Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge App
 
OSCM Unit 2_Operations Processes & Systems
OSCM Unit 2_Operations Processes & SystemsOSCM Unit 2_Operations Processes & Systems
OSCM Unit 2_Operations Processes & Systems
 
ANTI PARKISON DRUGS.pptx
ANTI         PARKISON          DRUGS.pptxANTI         PARKISON          DRUGS.pptx
ANTI PARKISON DRUGS.pptx
 
FICTIONAL SALESMAN/SALESMAN SNSW 2024.pdf
FICTIONAL SALESMAN/SALESMAN SNSW 2024.pdfFICTIONAL SALESMAN/SALESMAN SNSW 2024.pdf
FICTIONAL SALESMAN/SALESMAN SNSW 2024.pdf
 
Analyzing and resolving a communication crisis in Dhaka textiles LTD.pptx
Analyzing and resolving a communication crisis in Dhaka textiles LTD.pptxAnalyzing and resolving a communication crisis in Dhaka textiles LTD.pptx
Analyzing and resolving a communication crisis in Dhaka textiles LTD.pptx
 
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
TỔNG HỢP HƠN 100 ĐỀ THI THỬ TỐT NGHIỆP THPT TOÁN 2024 - TỪ CÁC TRƯỜNG, TRƯỜNG...
 
MOOD STABLIZERS DRUGS.pptx
MOOD     STABLIZERS           DRUGS.pptxMOOD     STABLIZERS           DRUGS.pptx
MOOD STABLIZERS DRUGS.pptx
 
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
 
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文會考英文
 
Đề tieng anh thpt 2024 danh cho cac ban hoc sinh
Đề tieng anh thpt 2024 danh cho cac ban hoc sinhĐề tieng anh thpt 2024 danh cho cac ban hoc sinh
Đề tieng anh thpt 2024 danh cho cac ban hoc sinh
 
VAMOS CUIDAR DO NOSSO PLANETA! .
VAMOS CUIDAR DO NOSSO PLANETA!                    .VAMOS CUIDAR DO NOSSO PLANETA!                    .
VAMOS CUIDAR DO NOSSO PLANETA! .
 
Andreas Schleicher presents at the launch of What does child empowerment mean...
Andreas Schleicher presents at the launch of What does child empowerment mean...Andreas Schleicher presents at the launch of What does child empowerment mean...
Andreas Schleicher presents at the launch of What does child empowerment mean...
 
How to Manage Website in Odoo 17 Studio App.pptx
How to Manage Website in Odoo 17 Studio App.pptxHow to Manage Website in Odoo 17 Studio App.pptx
How to Manage Website in Odoo 17 Studio App.pptx
 
Mattingly "AI & Prompt Design: Named Entity Recognition"
Mattingly "AI & Prompt Design: Named Entity Recognition"Mattingly "AI & Prompt Design: Named Entity Recognition"
Mattingly "AI & Prompt Design: Named Entity Recognition"
 
e-Sealing at EADTU by Kamakshi Rajagopal
e-Sealing at EADTU by Kamakshi Rajagopale-Sealing at EADTU by Kamakshi Rajagopal
e-Sealing at EADTU by Kamakshi Rajagopal
 
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPSSpellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
 
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjj
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjjStl Algorithms in C++ jjjjjjjjjjjjjjjjjj
Stl Algorithms in C++ jjjjjjjjjjjjjjjjjj
 
Improved Approval Flow in Odoo 17 Studio App
Improved Approval Flow in Odoo 17 Studio AppImproved Approval Flow in Odoo 17 Studio App
Improved Approval Flow in Odoo 17 Studio App
 
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
 

solutionA=  1    1    0    4    3    1    2    0 .pdf

  • 1. solution: A= 1 1 0 4 3 1 2 0 5 Finding the determinant of the matrix ? det A = -3 The determinant of A is non-zero, hence the inverse matrix A-1 exists. To find the inverse matrix was calculated the minors and cofactors of the matrix ? M1,1 = 3 1 0 5 = 15 C1,1 = (-1)1+1M1,1 = 15 M1,2 = 4 1 2 5 = 18
  • 2. C1,2 = (-1)1+2M1,2 = -18 M1,3 = 4 3 2 0 = -6 C1,3 = (-1)1+3M1,3 = -6 M2,1 = 1 0 0 5 = 5 C2,1 = (-1)2+1M2,1 = -5 M2,2 = 1 0 2 5 = 5 C2,2 = (-1)2+2M2,2 = 5 M2,3 = 1 1 2 0 = -2
  • 3. C2,3 = (-1)2+3M2,3 = 2 M3,1 = 1 0 3 1 = 1 C3,1 = (-1)3+1M3,1 = 1 M3,2 = 1 0 4 1 = 1 C3,2 = (-1)3+2M3,2 = -1 M3,3 = 1 1 4 3 = -1 C3,3 = (-1)3+3M3,3 = -1 Matrix of cofactors: C = 15 -18 -6 -5 5
  • 4. 2 1 -1 -1 Transpose of cofactor matrix: CT = 15 -5 1 -18 5 -1 -6 2 -1 Finding the inverse matrix. A-1 = CT = det A -5 5/3 -1/3 6 -5/3 1/3 2 -2/3 1/3 B) First, let's add the Identity Matrix to the right of our matrix 1 1
  • 5. 0 1 0 0 4 3 1 0 1 0 2 0 5 0 0 1 Now, let's do Gauss-Jordan Elimination on our new matrix... Add (-4 * row1) to row2 1 1 0 1 0 0 0 -1 1 -4 1 0 2 0 5 0
  • 6. 0 1 Add (-2 * row1) to row3 1 1 0 1 0 0 0 -1 1 -4 1 0 0 -2 5 -2 0 1 Divide row2 by -1 1 1 0 1 0 0 0 1 -1 4 -1 0
  • 7. 0 -2 5 -2 0 1 Add (2 * row2) to row3 1 1 0 1 0 0 0 1 -1 4 -1 0 0 0 3 6 -2 1 Divide row3 by 3 1 1 0 1 0 0 0 1
  • 8. -1 4 -1 0 0 0 1 2 -2/3 1/3 Add (1 * row3) to row2 1 1 0 1 0 0 0 1 0 6 -5/3 1/3 0 0 1 2 -2/3 1/3 Add (-1 * row2) to row1 1 0 0 -5
  • 9. 5/3 -1/3 0 1 0 6 -5/3 1/3 0 0 1 2 -2/3 1/3 The inverse matrix can now be found in the right 3 columns of our reduced row echelon matrix Here is the inverse matrix: -5 5/3 -1/3 6 -5/3 1/3 2 -2/3 1/3 A= 1 1 0 4 3 1 2 0
  • 10. 5 Solution solution: A= 1 1 0 4 3 1 2 0 5 Finding the determinant of the matrix ? det A = -3 The determinant of A is non-zero, hence the inverse matrix A-1 exists. To find the inverse matrix was calculated the minors and cofactors of the matrix ? M1,1 = 3 1 0 5 = 15 C1,1 = (-1)1+1M1,1 = 15 M1,2 = 4 1 2
  • 11. 5 = 18 C1,2 = (-1)1+2M1,2 = -18 M1,3 = 4 3 2 0 = -6 C1,3 = (-1)1+3M1,3 = -6 M2,1 = 1 0 0 5 = 5 C2,1 = (-1)2+1M2,1 = -5 M2,2 = 1 0 2 5 = 5 C2,2 = (-1)2+2M2,2 = 5 M2,3 = 1 1 2
  • 12. 0 = -2 C2,3 = (-1)2+3M2,3 = 2 M3,1 = 1 0 3 1 = 1 C3,1 = (-1)3+1M3,1 = 1 M3,2 = 1 0 4 1 = 1 C3,2 = (-1)3+2M3,2 = -1 M3,3 = 1 1 4 3 = -1 C3,3 = (-1)3+3M3,3 = -1 Matrix of cofactors: C = 15 -18
  • 13. -6 -5 5 2 1 -1 -1 Transpose of cofactor matrix: CT = 15 -5 1 -18 5 -1 -6 2 -1 Finding the inverse matrix. A-1 = CT = det A -5 5/3 -1/3 6 -5/3 1/3 2 -2/3 1/3 B)
  • 14. First, let's add the Identity Matrix to the right of our matrix 1 1 0 1 0 0 4 3 1 0 1 0 2 0 5 0 0 1 Now, let's do Gauss-Jordan Elimination on our new matrix... Add (-4 * row1) to row2 1 1 0 1 0 0 0 -1 1 -4 1 0 2
  • 15. 0 5 0 0 1 Add (-2 * row1) to row3 1 1 0 1 0 0 0 -1 1 -4 1 0 0 -2 5 -2 0 1 Divide row2 by -1 1 1 0 1 0 0 0 1 -1
  • 16. 4 -1 0 0 -2 5 -2 0 1 Add (2 * row2) to row3 1 1 0 1 0 0 0 1 -1 4 -1 0 0 0 3 6 -2 1 Divide row3 by 3 1 1 0 1 0
  • 17. 0 0 1 -1 4 -1 0 0 0 1 2 -2/3 1/3 Add (1 * row3) to row2 1 1 0 1 0 0 0 1 0 6 -5/3 1/3 0 0 1 2 -2/3 1/3 Add (-1 * row2) to row1 1
  • 18. 0 0 -5 5/3 -1/3 0 1 0 6 -5/3 1/3 0 0 1 2 -2/3 1/3 The inverse matrix can now be found in the right 3 columns of our reduced row echelon matrix Here is the inverse matrix: -5 5/3 -1/3 6 -5/3 1/3 2 -2/3 1/3 A= 1 1 0 4 3