Chapter 11: Q. 23 (page 756)

In Problems 9–24, use the following matrices to evaluate the given expression.
$A = [\begin{matrix} 0 & 3 & - 5 \\ 1 & 2 & 6 \end{matrix}]; B = [\begin{matrix} 4 & 1 & 0 \\ - 2 & 3 & - 2 \end{matrix}]; C = [\begin{matrix} 4 & 1 \\ 6 & 2 \\ - 2 & 3 \end{matrix}]$
role="math" localid="1647450119627" $C A - C B$

Short Answer

Expert verified

The evaluation of the expression $C A - C B$ is $[\begin{matrix} - 13 & 7 & - 12 \\ - 18 & 10 & - 14 \\ 17 & - 7 & 34 \end{matrix}]$

Step by step solution

Step 1. Given Information

The matrices:

$A = [\begin{matrix} 0 & 3 & - 5 \\ 1 & 2 & 6 \end{matrix}]; B = [\begin{matrix} 4 & 1 & 0 \\ - 2 & 3 & - 2 \end{matrix}]; C = [\begin{matrix} 4 & 1 \\ 6 & 2 \\ - 2 & 3 \end{matrix}]$

Step 2. Find CA

$C A = [\begin{matrix} 4 & 1 \\ 6 & 2 \\ - 2 & 3 \end{matrix}] [\begin{matrix} 0 & 3 & - 5 \\ 1 & 2 & 6 \end{matrix}] = [\begin{matrix} 4 (0) + 1 (1) & 4 (3) + 1 (2) & 4 (- 5) + 1 (6) \\ 6 (0) + 2 (1) & 6 (3) + 2 (2) & 6 (- 5) + 2 (6) \\ - 2 (0) + 3 (1) & - 2 (3) + 3 (2) & - 2 (- 5) + 3 (6) \end{matrix}] = [\begin{matrix} 1 & 14 & - 14 \\ 2 & 22 & - 18 \\ 3 & 0 & 28 \end{matrix}]$

Step 3. Find CB

$C B = [\begin{matrix} 4 & 1 \\ 6 & 2 \\ - 2 & 3 \end{matrix}] [\begin{matrix} 4 & 1 & 0 \\ - 2 & 3 & - 2 \end{matrix}] = [\begin{matrix} 4 (4) + 1 (- 2) & 4 (1) + 1 (3) & 4 (0) + 1 (- 2) \\ 6 (4) + 2 (- 2) & 6 (1) + 2 (3) & 6 (0) + 2 (- 2) \\ - 2 (4) + 3 (- 2) & - 2 (1) + 3 (3) & - 2 (0) + 3 (- 2) \end{matrix}] = [\begin{matrix} 14 & 7 & - 2 \\ 20 & 12 & - 4 \\ - 14 & 7 & - 6 \end{matrix}]$

Step 4. Find the resultant matrix

$C A - C B = [\begin{matrix} 1 & 14 & - 14 \\ 2 & 22 & - 18 \\ 3 & 0 & 28 \end{matrix}] - [\begin{matrix} 14 & 7 & - 2 \\ 20 & 12 & - 4 \\ - 14 & 7 & - 6 \end{matrix}] = [\begin{matrix} - 13 & 7 & - 12 \\ - 18 & 10 & - 14 \\ 17 & - 7 & 34 \end{matrix}]$

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Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find CA

Step 3. Find CB

Step 4. Find the resultant matrix

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In Problems 9–24, use the following matrices to evaluate the given expression.A=03-5126;B=410-23-2;C=4162-23role="math" localid="1647450119627" CA-CB

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find CA

Step 3. Find CB

Step 4. Find the resultant matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Theoretical and Mathematical Physics

Mechanics Maths

Discrete Mathematics

Study anywhere. Anytime. Across all devices.