Unit 1-6: Operations with Matrices

How could we organize the data?

How would you organize the date?

Concept

Add and Subtract Matrices

Substitution

Add corresponding elements.

Simplify.

Answer:

Add and Subtract Matrices

Answer: Since the dimensions of A are 2 × 3 and the dimensions of B are 2 × 2, these matrices cannot be subtracted.

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Example 2

A.

B.

C.

D.

Concept

Example 3 Multiply a Matrix by a Scalar

Substitution

Example 3 Multiply a Matrix by a Scalar

Multiply each element by 2.

Answer:

Simplify.

Concept

Example 4 Multi-Step Operations

Perform the scalar multiplication first. Then subtract the matrices.

Substitution

Distribute the scalars in each matrix.

4A – 3B

Example 4Multiply.

Subtract corresponding elements.

Answer:

Simplify.

Multi-Step Operations

Example 4

A.

B.

C.

D.

Example 5 Use Multi-Step Operations with Matrices

BUSINESS A small company makes unfinished desks and cabinets. Each item requires different amounts of hardware as shown in the matrices.

DESK

Short LongNailsScrews

CABINET

Short

LongNailsScrews

The company has orders for 3 desks and 4 cabinets. Express the company’s total needs for hardware in a single matrix.

Example 5 Use Multi-Step Operations with Matrices

Write matrices.

Multiply scalars.

Add matrices.

Answer:

Example 5 Use Multi-Step Operations with Matrices

Write matrices.

Multiply scalars.

Add matrices.

Short LongNailsScrews

Answer:

AssignmentPg. 175-177#2,3,5,8,10,12,13,26,30,33