Chapter 11: Q. 21 (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="1647448713874" $A C - 3 I_{2}$

Short Answer

Expert verified

The evaluation of the expression $A C - 3 I_{2}$ is $[\begin{matrix} 25 & - 9 \\ 4 & 20 \end{matrix}]$

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 AC

$A C = [\begin{matrix} 0 & 3 & - 5 \\ 1 & 2 & 6 \end{matrix}] [\begin{matrix} 4 & 1 \\ 6 & 2 \\ - 2 & 3 \end{matrix}] = [\begin{matrix} 0 (4) + 3 (6) + - 5 (- 2) & 0 (1) + 3 (2) + - 5 (3) \\ 1 (4) + 2 (6) + 6 (- 2) & 1 (1) + 2 (2) + 6 (3) \end{matrix}] = [\begin{matrix} 28 & - 9 \\ 4 & 23 \end{matrix}]$

Step 3. Find 3I2

$3 I_{2} = 3 [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] = [\begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}]$

Step 4. Find the resultant matrix

$A C - 3 I_{2} = [\begin{matrix} 28 & - 9 \\ 4 & 23 \end{matrix}] - [\begin{matrix} 3 & 0 \\ 0 & 3 \end{matrix}] = [\begin{matrix} 25 & - 9 \\ 4 & 20 \end{matrix}]$

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Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find AC

Step 3. Find 3I2

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="1647448713874" AC-3I2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find AC

Step 3. Find 3I2

Step 4. Find the resultant matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Applied Mathematics

Decision Maths

Statistics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.