Chapter 11: Q. 30 (page 756)

In Problems 25– 30, find the product.
$[\begin{matrix} 4 & - 2 & 3 \\ 0 & 1 & 2 \\ - 1 & 0 & 1 \end{matrix}] [\begin{matrix} 2 & 6 \\ 1 & - 1 \\ 0 & 2 \end{matrix}]$

Short Answer

Expert verified

The product of the matrices $[\begin{matrix} 4 & - 2 & 3 \\ 0 & 1 & 2 \\ - 1 & 0 & 1 \end{matrix}] [\begin{matrix} 2 & 6 \\ 1 & - 1 \\ 0 & 2 \end{matrix}]$ is $[\begin{matrix} 6 & 32 \\ 1 & 3 \\ - 2 & - 4 \end{matrix}]$

Step by step solution

Step 1. Given Information

The matrices:

$[\begin{matrix} 4 & - 2 & 3 \\ 0 & 1 & 2 \\ - 1 & 0 & 1 \end{matrix}] [\begin{matrix} 2 & 6 \\ 1 & - 1 \\ 0 & 2 \end{matrix}]$

Step 2. Observe the matrix

The first matrix is $3 \times 3$ matrix and the second matrix is $3 \times 2$ , so the resultant matrix will be of the form $3 \times 2$ matrix

Step 3. Find the product

$[\begin{matrix} 4 & - 2 & 3 \\ 0 & 1 & 2 \\ - 1 & 0 & 1 \end{matrix}] [\begin{matrix} 2 & 6 \\ 1 & - 1 \\ 0 & 2 \end{matrix}] = [\begin{matrix} 4 (2) + - 2 (1) + 3 (0) & 4 (6) + - 2 (- 1) + 3 (2) \\ 0 (2) + 1 (1) + 2 (0) & 0 (6) + 1 (- 1) + 2 (2) \\ - 1 (2) + 0 (1) + 1 (0) & - 1 (6) + 0 (- 1) + 1 (2) \end{matrix}] = [\begin{matrix} 6 & 32 \\ 1 & 3 \\ - 2 & - 4 \end{matrix}]$

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In Problems 25– 30, find the product.
$[\begin{matrix} 4 & - 2 & 3 \\ 0 & 1 & 2 \\ - 1 & 0 & 1 \end{matrix}] [\begin{matrix} 2 & 6 \\ 1 & - 1 \\ 0 & 2 \end{matrix}]$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Observe the matrix

Step 3. Find the product

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In Problems 25– 30, find the product.4-23012-101261-102

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Observe the matrix

Step 3. Find the product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 25– 30, find the product.
$[\begin{matrix} 4 & - 2 & 3 \\ 0 & 1 & 2 \\ - 1 & 0 & 1 \end{matrix}] [\begin{matrix} 2 & 6 \\ 1 & - 1 \\ 0 & 2 \end{matrix}]$