Matrices and linear algebra in Excel 2007

1. MATRICES AND LINEAR
ALGEBRA IN EXCEL 2007
CAROLINA MARIA CAMACHO ZAMBRANO
3rd CYCLE 2016-2
SYSTEMS ENGINEERING
EAN UNIVERSITY

2. How can excel studying motivate and help in
understanding and learning the matrix concept
and its associated operations?
Matrix is an associated concept in
programming and finance, so Excel can
help show the correlation between items,
and in this way, it can be a booster for
understanding and learning this notion
and its related operations.

3. 1. How to organize (enter) data into matrices?
•According to Wacha
(n.d.), in order to
organize data into
matrices, you type each
matrix info into each
cell, as you can see in the
image on the right.
Source:Wacha, n.d., online

4. 2. How to add matrices?
Step-by-step Instructions (Wacha, n.d.,online)
1. Enter the data of each matrix onto the worksheet.
2. Highlight another section of the worksheet that has the same
dimensions as the answer matrix.
3. Type: =(A2:C4)+(E2:G4) (This will appear in the formula bar.)
4. Since this answer will result in an array (matrix), you will need to:
CRTL+SHIFT+ENTER
Source:Wacha, n.d., online

5. 3. How to subtract matrices?
Step-by-step Instructions (Wacha, n.d.,online)
1. Enter the data of each matrix onto the worksheet.
2. Highlight another section of the worksheet that has the same
dimensions as the answer matrix.
3. Type: =(A2:C4)-(E2:G4) (This will appear in the formula bar.)
4. Since this answer will result in an array (matrix), you will need to:
CRTL+SHIFT+ENTER
Source:Wacha, n.d., online

6. 4. How to find the transpose of a matrix?
Step-by-step Instructions (Wacha, n.d.,online)
1. Enter the data of each matrix onto the worksheet.
2. Highlight another section of the worksheet that has the same dimensions as the answer
matrix.
NOTE: Since we are finding the transpose of a 3x2 matrix, the answer will be a 2x3
matrix. Recall that the transpose of a matrix swaps the given rows for columns and the
given columns for rows. So, if the given matrix as an order of RxC then its transpose will
have an order of CxR
3.Type: =TRANSPOSE(A2:B4)(This will appear in the formula bar.)
4. Since this answer will result in an array (matrix), you will need to: CRTL+SHIFT+ENTER
Source:Wacha, n.d., online

7. 5. How to multiply a matrix by a scalar (real number)?
Step-by-step Instructions (Wacha, n.d.,online)
1. Enter the data of each matrix onto the worksheet.
2. Highlight another section of the worksheet that has the same dimensions as the
answer matrix.
NOTE: Since we are multiplying a 4x3 matrix by the scalar, the answer will be a
4x3 matrix.
3. Type: =3*(A2:C5) (This will appear in the formula bar.)
4. Since this answer will result in an array (matrix), you will need to:
CRTL+SHIFT+ENTER
Source:Wacha, n.d., online

8. 6. How to multiply two matrices?
Step-by-step Instructions (Wacha, n.d.,online)
1. Enter the data of each matrix onto the worksheet.
2. Highlight another section of the worksheet that has the same dimensions as the
answer matrix.
NOTE: Since we are multiplying a 4x3 matrix by the scalar, the answer will be a
4x3 matrix.
3. Type: =3*(A2:C5) (This will appear in the formula bar.)
4. Since this answer will result in an array (matrix), you will need to:
CRTL+SHIFT+ENTER
Source:Wacha, n.d., online

9. 6. How to multiply two matrices?
Step-by-step Instructions (Wacha, n.d.,online)
1. Enter the data of each matrix onto the worksheet.
2. Highlight another section of the worksheet that has the same dimensions as the
answer matrix.
NOTE: Since we are multiplying a 4x3 matrix by the scalar, the answer will be a
4x3 matrix.
3. Type: =3*(A2:C5) (This will appear in the formula bar.)
4. Since this answer will result in an array (matrix), you will need to:
CRTL+SHIFT+ENTER
Source:Wacha, n.d., online

10. 7. How to find the inverse of a square matrix?
Step-by-step Instructions (Wacha, n.d.,online)
1. Enter the data of each matrix onto the worksheet.
2. Highlight another section of the worksheet that has the same dimensions as the
answer matrix.
NOTE: Since we are multiplying a 4x3 matrix by the scalar, the answer will be a
4x3 matrix.
3. Type: =3*(A2:C5) (This will appear in the formula bar.)
4. Since this answer will result in an array (matrix), you will need to:
CRTL+SHIFT+ENTER
Source:Wacha, n.d., online

11. 8. How to find the determinant of a square matrix:
Step-by-step Instructions (Wacha, n.d.,online)
1. Enter the data of each matrix onto the worksheet.
2. Highlight another section of the worksheet that has the same dimensions as the answer
matrix.
NOTE: Since we are finding the determinant of a matrix, we need to highlight just one
cell (F2 in the diagram).
3. Type: =MDETERM(A2:C4;E2:H4) (This will appear in the formula bar.)
4. Since this answer will result in an array (matrix), you will need to: CRTL+SHIFT+ENTER
NOTE: Recall that multiplication of matrices is NOT commutative. So, if we reversed the
two matrices (BA), we would be attempting to multiply a 3x4 matrix by a 3x3 matrix.
Since the two middle numbers do not match, the multiplication cannot be completed.
Source:Wacha, n.d., online

12. 9. How to use inverse matrices to solve systems of equations?
Step-by-step Instructions (Wacha, n.d.,online)
1. Enter the data of the coefficient matrix onto the worksheet (cells
A2 to E6).
2. Find the determinant of the coefficient matrix:
Highlight another section of the worksheet (cell G2) where the
determinant will be displayed.
Type: =MDETERM(A2:E6)
Remember to: ENTER . . . or . . . CRTL+SHIFT+ENTER
NOTE: A matrix will have no inverse if its determinant is zero (0). If
the coefficient matrix of a system of equations has a determinant
equal to zero (0), the system will not have a unique solution.
However, you will need to determine whether the given system of
equations has a general solution or no solution at all by completing
the Gauss-Jordan Elimination (row operations) method.
Remember to: CRTL+SHIFT+ENTER

13. 9. How to use inverse matrices to solve systems of equations?
Source:Wacha, n.d., online

14. 9. How to use inverse matrices to solve systems of equations?
Step-by-step Instructions (Wacha, n.d.,online)
3. Find the inverse of this coefficient matrix: Highlight
another section of the worksheet that has the
dimensions as the inverse. Since we are finding the
inverse of a 5x5 matrix, its inverse will also be 5x5 matrix.
Type: =MINVERSE(A2:E6)
Remember to: CRTL+SHIFT+ENTER
4. Enter the data of the constant matrix onto the worksheet
(cells O2 to O6).

15. 9. How to use inverse matrices to solve systems of equations?
Source:Wacha, n.d., online

16. 9. How to use inverse matrices to solve systems of equations?
Step-by-step Instructions (Wacha, n.d.,online)
5. Multiply the “inverse matrix” (cells I2 to M6) by the “constant
matrix” (cells O2 to O6):
Highlight another section of the worksheet that has the dimensions
of the answer matrix. For this example, we will be multiplying a 5x5
matrix with a 5x1 matrix which will result in a product that should
be a 5x1 matrix.
Type: =MMULT(I2:M6,O2:O6) (This will appear in the formula bar.)
Remember to: CRTL+SHIFT+ENTERFind the inverse of this
coefficient matrix:
6. The final solution for the system of equations will appear in resulting
matrix. For this example, in the matrix that appears in cells R2 to
R6.Therefore, the solutions for the given system is:
a = 1 b = 2 c = 3 d = 4 e = 5

17. 9. How to use inverse matrices to solve systems of equations?
Source:Wacha, n.d., online

18. References
• Canahuire C., A. (February 2010) Cálculo Matricial en el Excel. Retrieved
from: https://goo.gl/VMKfWP
• García, J. (2013). Operaciones básicas de matrices en Excel. Retrieved from:
http://goo.gl/6ha1MY
• Wacha, D. (n.d.) Matrix (Array) Operations. Monmouth University.
Mathematics Department. Retrieved from http://goo.gl/MwbzjN

19. THANKYOU!