Chapter 11: Q. 22 (page 756)

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

Short Answer

Expert verified

The evaluation of the expression $C A + 5 I_{3}$ is $[\begin{matrix} 6 & 14 & - 14 \\ 2 & 27 & - 18 \\ 3 & 0 & 33 \end{matrix}]$

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 5I3

$5 I_{3} = 5 [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] = [\begin{matrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{matrix}]$

Step 4. Find the resultant matrix

$C A + 5 I_{3} = [\begin{matrix} 1 & 14 & - 14 \\ 2 & 22 & - 18 \\ 3 & 0 & 28 \end{matrix}] + [\begin{matrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{matrix}] = [\begin{matrix} 6 & 14 & - 14 \\ 2 & 27 & - 18 \\ 3 & 0 & 33 \end{matrix}]$

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find CA

Step 3. Find 5I3

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=4162-23CA+5I3

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find CA

Step 3. Find 5I3

Step 4. Find the resultant matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Pure Maths

Applied Mathematics

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

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