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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![Given the matrices:
\[ A = \begin{bmatrix} 1 & -1 & 2 \\ 3 & 0 & 5 \end{bmatrix} \]
and
\[ B = \begin{bmatrix} -1 & -3 & 2 \\ 2 & 4 & 5 \\ 0 & 2 & -2 \end{bmatrix} \]
find \( AB \).
Answer choices:
1.
\[ \begin{bmatrix} 3 & -3 & -7 \\ -3 & -1 & 4 \end{bmatrix} \]
2.
\[ \begin{bmatrix} 3 & 3 & 5 \\ -2 & 6 & 4 \end{bmatrix} \]
3.
\[ \begin{bmatrix} -3 & -3 & -7 \\ -3 & 1 & -4 \end{bmatrix} \]
4.
\[ \begin{bmatrix} 3 & -3 & 3 \\ -3 & 1 & -7 \end{bmatrix} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a93d8bf-dcec-4fd1-a13b-11f29e84e363%2Ffe603693-90f9-49c5-b709-c8346569b77c%2Fzwy08g_processed.png&w=3840&q=75)
Transcribed Image Text:Given the matrices:
\[ A = \begin{bmatrix} 1 & -1 & 2 \\ 3 & 0 & 5 \end{bmatrix} \]
and
\[ B = \begin{bmatrix} -1 & -3 & 2 \\ 2 & 4 & 5 \\ 0 & 2 & -2 \end{bmatrix} \]
find \( AB \).
Answer choices:
1.
\[ \begin{bmatrix} 3 & -3 & -7 \\ -3 & -1 & 4 \end{bmatrix} \]
2.
\[ \begin{bmatrix} 3 & 3 & 5 \\ -2 & 6 & 4 \end{bmatrix} \]
3.
\[ \begin{bmatrix} -3 & -3 & -7 \\ -3 & 1 & -4 \end{bmatrix} \]
4.
\[ \begin{bmatrix} 3 & -3 & 3 \\ -3 & 1 & -7 \end{bmatrix} \]
![The problem provides two matrices, \( A \) and \( B \), and asks to find \( 6A - 4B \).
Matrix \( A \) is:
\[
A = \begin{bmatrix}
-5 & 6 & -8 \\
9 & -4 & -5
\end{bmatrix}
\]
Matrix \( B \) is:
\[
B = \begin{bmatrix}
8 & 6 & -5 \\
5 & -7 & 3
\end{bmatrix}
\]
The task is to compute \( 6A - 4B \). Then, four answer options are provided, each containing a matrix. We need to determine which matrix corresponds to the calculation \( 6A - 4B \).
Given Options:
1.
\[
\begin{bmatrix}
-62 & 12 & -28 \\
34 & 4 & -42
\end{bmatrix}
\]
2.
\[
\begin{bmatrix}
-62 & -12 & -28 \\
34 & 4 & -42
\end{bmatrix}
\]
3.
\[
\begin{bmatrix}
-62 & 60 & 28 \\
34 & -52 & -42
\end{bmatrix}
\]
4.
\[
\begin{bmatrix}
62 & 12 & -28 \\
34 & -52 & -42
\end{bmatrix}
\]
To find the solution, each element of \( A \) is multiplied by 6, and each element of \( B \) is multiplied by 4. Then, the resulting matrix from \( 4B \) is subtracted from the resulting matrix from \( 6A \). Compare the result with the given options to find the correct answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8a93d8bf-dcec-4fd1-a13b-11f29e84e363%2Ffe603693-90f9-49c5-b709-c8346569b77c%2F4bgnl28_processed.png&w=3840&q=75)
Transcribed Image Text:The problem provides two matrices, \( A \) and \( B \), and asks to find \( 6A - 4B \).
Matrix \( A \) is:
\[
A = \begin{bmatrix}
-5 & 6 & -8 \\
9 & -4 & -5
\end{bmatrix}
\]
Matrix \( B \) is:
\[
B = \begin{bmatrix}
8 & 6 & -5 \\
5 & -7 & 3
\end{bmatrix}
\]
The task is to compute \( 6A - 4B \). Then, four answer options are provided, each containing a matrix. We need to determine which matrix corresponds to the calculation \( 6A - 4B \).
Given Options:
1.
\[
\begin{bmatrix}
-62 & 12 & -28 \\
34 & 4 & -42
\end{bmatrix}
\]
2.
\[
\begin{bmatrix}
-62 & -12 & -28 \\
34 & 4 & -42
\end{bmatrix}
\]
3.
\[
\begin{bmatrix}
-62 & 60 & 28 \\
34 & -52 & -42
\end{bmatrix}
\]
4.
\[
\begin{bmatrix}
62 & 12 & -28 \\
34 & -52 & -42
\end{bmatrix}
\]
To find the solution, each element of \( A \) is multiplied by 6, and each element of \( B \) is multiplied by 4. Then, the resulting matrix from \( 4B \) is subtracted from the resulting matrix from \( 6A \). Compare the result with the given options to find the correct answer.
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