FIND BOTH PLEASE!! its in the question it tells you what it needs! ## Matrix Subtraction and Multiplication### Problem Statement:Compute $ A - 4I_3 $ and $ (4I_3)A $, where $ A $ is given by:\[ A = \begin{bmatrix}6 & -2 & 4 \\-4 & 3 & -6 \\-3 & 1 & 3 \end{bmatrix} \]### Equation and Matrix:To find $ A - 4I_3 $, we need to subtract $ 4I_3 $ from matrix $ A $, where $ I_3 $ is the 3x3 identity matrix scaled by 4.#### Identity Matrix $ I_3 $:\[I_3 =\begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \end{bmatrix}\]#### Scaled Identity Matrix $ 4I_3 $:\[4I_3 =\begin{bmatrix}4 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 4\end{bmatrix}\]#### Subtracting $ 4I_3 $ from $ A $:\[A - 4I_3 =\begin{bmatrix}6 & -2 & 4 \\-4 & 3 & -6 \\-3 & 1 & 3 \end{bmatrix}-\begin{bmatrix}4 & 0 & 0 \\0 & 4 & 0 \\0 & 0 & 4\end{bmatrix}\]### Final Calculation:Perform the subtraction element-wise:\[A - 4I_3 =\begin{bmatrix}6 - 4 & -2 - 0 & 4 - 0 \\-4 - 0 & 3 - 4 & -6 - 0 \\-3 - 0 & 1 - 0 & 3 - 4\end{bmatrix}=\begin{bmatrix}2 & -2 & 4 \\-4 & -1 & -6 \\-3 & 1 & -1\end{bmatrix}\]So

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Answered: Compute A-413 and (413)A, where A =…

Math

Algebra

Compute A-413 and (413)A, where A = A-413 = 6 - 4 - 3 - 2 4 3 - 6 1 3

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

FIND BOTH PLEASE!! its in the question it tells you what it needs!

## Matrix Subtraction and Multiplication

### Problem Statement:
Compute $ A - 4I_3 $ and $ (4I_3)A $, where $ A $ is given by:

\[
A =
\begin{bmatrix}
6 & -2 & 4 \\
-4 & 3 & -6 \\
-3 & 1 & 3
\end{bmatrix}
\]

### Equation and Matrix:

To find $ A - 4I_3 $, we need to subtract $ 4I_3 $ from matrix $ A $, where $ I_3 $ is the 3x3 identity matrix scaled by 4.

#### Identity Matrix $ I_3 $:
\[
I_3 =
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\]

#### Scaled Identity Matrix $ 4I_3 $:
\[
4I_3 =
\begin{bmatrix}
4 & 0 & 0 \\
0 & 4 & 0 \\
0 & 0 & 4
\end{bmatrix}
\]

#### Subtracting $ 4I_3 $ from $ A $:
\[
A - 4I_3 =
\begin{bmatrix}
6 & -2 & 4 \\
-4 & 3 & -6 \\
-3 & 1 & 3
\end{bmatrix}
-
\begin{bmatrix}
4 & 0 & 0 \\
0 & 4 & 0 \\
0 & 0 & 4
\end{bmatrix}
\]

### Final Calculation:
Perform the subtraction element-wise:

\[
A - 4I_3 =
\begin{bmatrix}
6 - 4 & -2 - 0 & 4 - 0 \\
-4 - 0 & 3 - 4 & -6 - 0 \\
-3 - 0 & 1 - 0 & 3 - 4
\end{bmatrix}
=
\begin{bmatrix}
2 & -2 & 4 \\
-4 & -1 & -6 \\
-3 & 1 & -1
\end{bmatrix}
\]

So

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