1. 25. Basic matrix operations

2. Matrix
A matrix is a rectangular array of numbers in rows and columns.
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3. Dimensions
The dimensions of a matrix with m rows and n columns are m X n.
The matrix has 3 rows and 2 columns so the dimensions are 3 X 2.
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4. 2 3 −1 0 8 1.2 Elements The numbers in a matrix are its elements.
Elements are identified by their row and column. Thus, element 3,2 is 1.2.
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5. Equal Matrices
Equal matrices have the same dimensions and the elements in corresponding positions are equal.

6. Scalar multiplication
In matrix algebra, a real number is often called a scalar. To perform scalar multiplication, you multiply each element in the matrix by the scalar.

7. Properties of Matrices
Associative Property of Addition
(A + B) + C = A + (B + C)
Commutative Property of Addition
A + B = B + A
We will see tomorrow that matrices do not have the commutative property of multiplication
Distributive Property of Addition/Subtraction
k(A + B) = kA + kB
k(A – B) = kA – kB

8. Adding and subtracting matrices
To add or subtract two matrices, simply add or subtract corresponding elements.
You can add or subtract matrices only if they have the same dimensions.

9. Try this!
Perform the indicated operation, if possible.
6 −
− −4 −

10. TRY this!
Perform the indicated operations, if possible.
−7 6 −1 4
− −5

11. Multi-step problem
Two pet stores sell both dogs and cats. Sales from each store for last month and this month are shown below:
Organize the data into matrices, then write and interpret a matrix giving the average monthly sales for the two month period.
Last Month: Store 1 sold 42 dogs, 33 cats. Store 2 sold 56 dogs, 21 cats.
This Month: Store 1 sold 36 dogs, 51 cats. Store 2 sold 48 dogs, 37 cats.

12. One More!
Solve the matrix equation for x and y.
−2 3 −2𝑥 1 7 − 1 −6 −5𝑦 4 = − −6

13. On your calculator
Let’s see how to input matrices in the calculator