A matrix is an ordered set of numbers listed in
rectangular form
Matrix A has 2 rows and 3 columns.
We say it is a 2x3 mat...
B is a row matrix.
C is a column matrix.
This is the 3x3 zero-matrix.
I is the 3x3 Identity matrix.
and are opposite matri...
We can sum matrices of the same order.
Multiplication of a matrix by a scalar
=3
To multiply matrices, we multiply rows into columns:
2 x 3 3x 2
=
2x 2
=
What special name has the answer?
Determinant of a matrix
Determinant of a matrix is a number calculated
from the elements of the matrix.
A =
det A=
Determinant of a 3x3 matrix
Find the determinant of:
If P= , find the value of x for which
|P| = 0.
If the determinant of a matrix is zero , 
the matrix is called a singular m...
Inverse of a matrix
Only square matrices have inverses.
Not all square matrices have inverses.
matrix A has an inverse A­1...
2x2 matrices:
or using GDC: x-1
key
3x3 matrices:
using GDC: x-1
key
Solutions of systems of linear equations
Using matrices we can rewrite these equations as:
A X = B
A­1
(AX) = A­1
B
(A­1
 ...
   X  = A­1
BA       X  =  B ⇒
X
⇒ x = 3  , y = 1 
Given the simultaneous equations:
write them in matrix form and find x, y and z.
using GDC :
Use your GDC to find the inverse of the matrix
Hence, solve the simultaneous equations:
4 11 5
1 4 2
1 2 1
4 x + 11 y + 5 ...
The matrix A =
2 0 2
5 1 0
­1 4 a
a) Find an expression in terms of a for detA.
b) Find the value of a for which A-1
does ...
Exercise Book page 336 Ex 1 a), 2 and 5
page 337 : EX8, 10,
revision exercise 12 page 339
IB Maths SL Matrices
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IB Maths SL Matrices

  1. 1. A matrix is an ordered set of numbers listed in rectangular form Matrix A has 2 rows and 3 columns. We say it is a 2x3 matrix. order 2x3
  2. 2. B is a row matrix. C is a column matrix. This is the 3x3 zero-matrix. I is the 3x3 Identity matrix. and are opposite matrices.
  3. 3. We can sum matrices of the same order. Multiplication of a matrix by a scalar =3
  4. 4. To multiply matrices, we multiply rows into columns: 2 x 3 3x 2 = 2x 2 = What special name has the answer?
  5. 5. Determinant of a matrix Determinant of a matrix is a number calculated from the elements of the matrix. A = det A=
  6. 6. Determinant of a 3x3 matrix
  7. 7. Find the determinant of:
  8. 8. If P= , find the value of x for which |P| = 0. If the determinant of a matrix is zero ,  the matrix is called a singular matrix
  9. 9. Inverse of a matrix Only square matrices have inverses. Not all square matrices have inverses. matrix A has an inverse A­1         |A| ≠ 0 singular matrices have no inverse
  10. 10. 2x2 matrices: or using GDC: x-1 key 3x3 matrices: using GDC: x-1 key
  11. 11. Solutions of systems of linear equations Using matrices we can rewrite these equations as: A X = B A­1 (AX) = A­1 B (A­1  A) X  = A­1 B I   X  = A­1 B    X  = A­1 B
  12. 12.    X  = A­1 BA       X  =  B ⇒ X ⇒ x = 3  , y = 1 
  13. 13. Given the simultaneous equations: write them in matrix form and find x, y and z.
  14. 14. using GDC :
  15. 15. Use your GDC to find the inverse of the matrix Hence, solve the simultaneous equations: 4 11 5 1 4 2 1 2 1 4 x + 11 y + 5 z = 2     x + 4  y + 2 z =  1    x + 2  y + 1  z =  4
  16. 16. The matrix A = 2 0 2 5 1 0 ­1 4 a a) Find an expression in terms of a for detA. b) Find the value of a for which A-1 does not exist. c) Solve the equation A when a = 0 giving your answers correct to 3 s.f.
  17. 17. Exercise Book page 336 Ex 1 a), 2 and 5 page 337 : EX8, 10, revision exercise 12 page 339

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