Block Math III.Introduction to Matrices

Name Date: ______Block Math III.Introduction to Matrices

A matrix is a rectangular arrangement of numbers in ______and ______.

The dimensions of the matrix are read in order as ______by ______.

If two matrices have the same dimensions and the same entries (called elements) in corresponding positions, then those matrices are said to be ______.

Create your own example of equal matrices here:

Matrices Operations Two or more matrices can be added or subtracted only if they have the same ______. To add or subtract matrices, simply add or subtract the ______.

In matrix Algebra, a real number is called a ______. To multiply a matrix by a scalar, multiply

______in the matrix by the scalar. This process is called scalar multiplication. 1 4  3 Find the product o:f   . 2 7 2 

Note: Matrix operations follow the order of operations rules. Perform the indicated operations. 1  1  7 3  1. 2 2      5 1  3 4 

1 骣轾4 5 1 轾- 2 3 - 5 2. 琪犏- 犏 = 2 桫臌7 4 2 臌 5- 1 - 12

To solve a matrix equation: 1. Simplify one or both sides of the equation using matrix operations as needed.

2. Set ______equal to each other and solve for the variable.

Solve for x and y:

01a11221753170a7b23c52fdb245fc14.doc 5/7/2018 轾6 5 轾 6 5 犏犏犏x+8 4= 犏 14 - x 4 臌犏0 2y- 1 臌犏 0 - 13 - y

The seniors are planning a trip for Spring Break. They have contacted three lodges in the vicinity to inquire about rates. They found that Rainbow Lodge charges $13.00 per person per day for lodging, $20.00 per day for food, and $5.00 per person for use of the recreational facilities. Rivers Lodge charges $12.50 for lodging,

$19.50 for meals, and $7.50 for use of the recreational facilities. Wolf Lodge charges $20.00 per night for lodging, $18.00 per day for meals, and no extra charge for using the recreational facilities. Trout Lodge charges a flat rate of $40.00 per day for lodging (meals included) and no additional fee for use of the recreational facilities. a. Display this information in a matrix, C. The rows and columns have been labeled for you.

Lodging Food Recreation Rainbow Lodge

Rivers Lodge

Wolf Lodge

Trout Lodge

b. State the values of C21 and C43.

c. Interpret C13 and C31.

Let A, B, and C be matrices and k be a scalar.

Properties of Matrix Addition Associative Property of Matrix Addition (A + B) + C = ______

Commutative Property of Addition A + B = ______

Distributive Property of Addition k(A + B) = ______

01a11221753170a7b23c52fdb245fc14.doc 5/7/2018 Distributive Property of Subtraction k(A - B) = ______

Multiplying Matrices

In order to multiply matrices A X B, the number of ______in A must equal the number of

______in B. If the product is defined, the solution matrix will have the same number of ______as A, and the same number of ______as B.

State whether the product is defined. 1. A: 3 X 2; B: 4 X 3 AB? BA?

2. A: 3 X 3; B: 3 X 2 AB? BA?

In order to find the product of two matrices, A X B, multiply the rows in A times the columns in B.

轾6 2 轾-1 2 犏-1 3 3. A = 犏 B = 犏 , find AB. 臌5- 2 臌犏0- 4

轾4 4. A = [7 3] B = 犏 , find AB and BA. 臌-1

轾4- 3 轾1 7 轾3- 5 - 2 5. A = 犏 B = 犏 C = 犏 , find (A+B)C. Also find AC +BC. 臌-1 2 臌-4 - 2 臌1 0 6

Let A, B, and C be matrices and k be a scalar.

Properties of Matrix Multiplication Associative Property of Matrix Multiplication A(BC) = ______

Left Distributive Property A(B+C) = ______

Right Distributive Property (A+B)C = ______

Associative Property of Scalar Multiplication k(AB) = ______= ______

01a11221753170a7b23c52fdb245fc14.doc 5/7/2018 NOTE: There is NO Commutative Property of Multiplication for Matrices; generally ______.

01a11221753170a7b23c52fdb245fc14.doc 5/7/2018