1. Precalculus Lesson 7.2 Matrix Algebra 4/6/2017 8:43 PM
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2. Quick Review

3. What you’ll learn about
Matrices
Matrix Addition and Subtraction
Matrix Multiplication
Identity and Inverse Matrices
Determinant of a Square Matrix
Applications
… and why
Matrix algebra provides a powerful technique to manipulate large data sets and solve the related problems that are modeled by the matrices.

4. Matrix

5. Matrix Vocabulary
Each element, or entry, aij, of the matrix uses double subscript notation.
The row subscript is the first subscript i, and the column subscript is j.
The element aij is the ith row and the jth
column.
In general, the order of an m × n matrix is
m×n.

6. Example Determining the Order of a Matrix

7. Matrix Addition and Matrix Subtraction

8. Example Matrix Addition

9. Example Using Scalar Multiplication

10. The Zero Matrix
Example:

11. Additive Inverse

12. Example Using Additive Inverse

13. Matrix Multiplication

14. Example Matrix Multiplication

15. Identity Matrix

16. Inverse of a Square Matrix

17. Example Inverse of a Square Matrices
Yes

18. Inverse of a 2 × 2 Matrix

19. Determinant of a Square Matrix
Refer to text pg 583

20. Inverses of n × n Matrices
An n × n matrix A has an inverse if and only if
det A ≠ 0.

21. Example Finding Inverse Matrices

22. Properties of Matrices
Let A, B, and C be matrices whose orders are such that
the following sums, differences, and products are defined.
1. Commutative property
Addition: A + B = B + A
Multiplication: Does not hold in general
2. Associative property
Addition: (A + B) + C = A + (B + C)
Multiplication: (AB)C = A(BC)
3. Identity property
Addition: A + 0 = A
Multiplication: A·In = In·A = A

23. Properties of Matrices
Let A, B, and C be matrices whose orders are such that
the following sums, differences, and products are defined.
4. Inverse property
Addition: A + (-A) = 0
Multiplication: AA-1 = A-1A = In |A|≠0
5. Distributive property
Multiplication over addition: A(B + C) = AB + AC
(A + B)C = AC + BC
Multiplication over subtraction: A(B - C) = AB - AC
(A - B)C = AC - BC

24. Homework:
Text pg588/589 Exercises
#2, 4, 14, 20, 24, and 34