The document covers various aspects of matrix algebra, including operations such as matrix addition, scalar-matrix multiplication, and matrix multiplication. It provides examples and solutions for computing the products of matrices and highlights important algebraic properties, including the transpose of a matrix. Additionally, the document appears to involve group exercises focused on solving problems related to matrix expressions.

1. MATRIX ALGEBRA
MS. MARIMAR B. BALDOZA
Discussant
MATH ED 207 - LINEAR ALGEBRA

2. MATRIX ALGEBRA
MATRIX ADDITION
SCALAR-MATRIX MULTIPLICATION
MATRIX MULTIPLICATION
MATRIX TRANSPOSE

3. Matrix Addition

4. Example
Example
1
2
Solution:
Solution

5. Scalar-Matrix Multiplication

6. Example
a
b
Compute 5A and 3A - 2B:
Solution:

7. Algebraic Properties of Matrix Addition/Scalar-Matrix
Multiplication

8. Example
Solution:

9. Matrix Multiplication

10. Example 1 1
2
For A and B below, compute AB and BA.
Solution:
On the other hand, BA is
not defined. B has 4
columns and A has 2
rows.

11. Detailed Solution

12. Example 2 1
2
For A and B below, compute AB and BA.
Solution:

13. Detailed Solution

14. Example 2 1
2
For A and B below, compute AB and BA.
Solution:

15. Detailed Solution

16. Example 2 1
2
For A and B below, compute AB and BA.

17. Algebraic Properties of Matrix Multiplication

18. Matrix Transpose

19. Examples:

20. Thus forming the transpose of a matrix A can be viewed as
“flipping” A about its main diagonal, or as “rotates” A through
180° about the line containing the main diagonal.

21. 1
2
For A and B below, compute AB and BA.
then,

22. Algebraic Properties of Matrix Transpose

23. Example:

24. Thank
Thank
Thank
you!
you!
you!

25. GROUP 1:
Solve for matrix A.

26. Simplify the given expression where A, B and C are matrices.
GROUP 2:

27. Solve for matrix A.
GROUP 3:

28. GROUP 4:

29. Solve for matrix A.
GROUP 5: