Chapter7: Systems Of Equations And Inequalities
Section7.7: Solving Systems With Inverses
Problem 4SE: Can a matrix with an entire column of zeros have an inverse? Explain why or why not.
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Question
![The image contains two matrices, [B] and [A], along with an expression for a matrix operation.
Matrix [B] is a 5x2 matrix:
\[
[B] = \begin{bmatrix}
0 & -8 \\
10 & -3 \\
8 & -9 \\
-10 & 6 \\
-1 & -2 \\
\end{bmatrix}
\]
Matrix [A] is also a 5x2 matrix:
\[
[A] = \begin{bmatrix}
7 & 9 \\
6 & 5 \\
10 & 1 \\
-7 & -1 \\
-8 & -6 \\
\end{bmatrix}
\]
The expression provided is for calculating \( 4[B] + 3[A] \). There is a blank 5x2 matrix template shown for the result.
To solve \( 4[B] + 3[A] \), multiply each entry of matrix [B] by 4 and each entry of matrix [A] by 3, then add the resulting matrices together.
The steps to compute one element \( (i, j) \) of the resulting matrix are:
\[ (4 \times B_{ij}) + (3 \times A_{ij}) \]
For example, the first element is calculated as:
\[ (4 \times 0) + (3 \times 7) = 0 + 21 = 21\]
Continue this process for each element to fill the blank matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F723d4455-88a3-4468-800e-ec0ca31b017d%2Fd6e82767-fad1-42b4-8867-88b92008a980%2Fjkivn5a_processed.png&w=3840&q=75)
Transcribed Image Text:The image contains two matrices, [B] and [A], along with an expression for a matrix operation.
Matrix [B] is a 5x2 matrix:
\[
[B] = \begin{bmatrix}
0 & -8 \\
10 & -3 \\
8 & -9 \\
-10 & 6 \\
-1 & -2 \\
\end{bmatrix}
\]
Matrix [A] is also a 5x2 matrix:
\[
[A] = \begin{bmatrix}
7 & 9 \\
6 & 5 \\
10 & 1 \\
-7 & -1 \\
-8 & -6 \\
\end{bmatrix}
\]
The expression provided is for calculating \( 4[B] + 3[A] \). There is a blank 5x2 matrix template shown for the result.
To solve \( 4[B] + 3[A] \), multiply each entry of matrix [B] by 4 and each entry of matrix [A] by 3, then add the resulting matrices together.
The steps to compute one element \( (i, j) \) of the resulting matrix are:
\[ (4 \times B_{ij}) + (3 \times A_{ij}) \]
For example, the first element is calculated as:
\[ (4 \times 0) + (3 \times 7) = 0 + 21 = 21\]
Continue this process for each element to fill the blank matrix.
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