Chapter 4: Q46. (page 181)

Determine whether each matrix product is defined. If so, state the dimensions of the product.
$A_{2 \times 3} \cdot B_{3 \times 2}$

Short Answer

Expert verified

Matrix product of given matrices is defined.

Product matrix has 2 rows and 2 columns.

Step by step solution

- Write condition for matrix product to be defined.

For two matrices $A$ and $B$ , the product $A \cdot B$ is defined when number of columns of matrix $A$ is equal to the number of rows of matrix $B$ .

- Write dimensions of given matrices

Matrix $A$ has 2 rows and 3 columns and matrix $B$ has 3 rows and 2 columns.

- Check multiplication is defined or not

As, number of columns of matrix $A$ is equal to the number of rows of matrix $B$ .

So multiplication is defined.

- Write dimension of product matrix

When multiplication is defined then resultant matrix $A \cdot B$ has number of rows equal to the number of rows of matrix $A$ and its number of column is equal to the number of columns of matrix $B$

So product of given two matrices gives a matrix which has 2 rows and 2 columns.

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Determine whether each matrix product is defined. If so, state the dimensions of the product.
$A_{2 \times 3} \cdot B_{3 \times 2}$

Short Answer

Step by step solution

- Write condition for matrix product to be defined.

- Write dimensions of given matrices

- Check multiplication is defined or not

- Write dimension of product matrix

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Determine whether each matrix product is defined. If so, state the dimensions of the product.A2×3·B3×2

Short Answer

Step by step solution

- Write condition for matrix product to be defined.

- Write dimensions of given matrices

- Check multiplication is defined or not

- Write dimension of product matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Applied Mathematics

Geometry

Probability and Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Determine whether each matrix product is defined. If so, state the dimensions of the product.
$A_{2 \times 3} \cdot B_{3 \times 2}$