Chapter 11: Q. 24 (page 756)

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

Short Answer

Expert verified

The evaluation of the expression $A C + B C$ is $[\begin{matrix} 50 & - 3 \\ 18 & 21 \end{matrix}]$

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 BC

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

Step 4. Find the resultant matrix

$A C + B C = [\begin{matrix} 28 & - 9 \\ 4 & 23 \end{matrix}] + [\begin{matrix} 22 & 6 \\ 14 & - 2 \end{matrix}] = [\begin{matrix} 50 & - 3 \\ 18 & 21 \end{matrix}]$

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find AC

Step 3. Find BC

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=4162-23AC+BC

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Find AC

Step 3. Find BC

Step 4. Find the resultant matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Decision Maths

Applied Mathematics

Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

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