20) Which of the following matrices has an inverse? 20) -2 1 A) B) C) 53.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
#20
![**Matrix Multiplication and Inverse Problems**
---
**Matrix Multiplication**
Find the matrix product mentally, without the use of a calculator or pencil-and-paper calculations.
**18)** Calculate the product of the matrices:
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{bmatrix}
\]
A) \[
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{bmatrix}
\]
B) \([1]\)
C) \[
\begin{bmatrix}
9 & 8 & 7 \\
6 & 5 & 4 \\
3 & 2 & 1
\end{bmatrix}
\]
D) \[
\begin{bmatrix}
1 & -2 & 3 \\
-4 & 5 & -6 \\
7 & -8 & 9
\end{bmatrix}
\]
Correct answer: ___
---
**Matrix Inverse**
Find the inverse, if it exists, of the given matrix:
**19)**
\[
\begin{bmatrix}
-6 & -6 \\
-5 & -5
\end{bmatrix}
\]
A) \[
\begin{bmatrix}
-\frac{5}{11} & \frac{6}{11} \\
\frac{5}{11} & -\frac{6}{11}
\end{bmatrix}
\]
B) \[
\begin{bmatrix}
\frac{5}{11} & -\frac{6}{11} \\
-\frac{5}{11} & \frac{6}{11}
\end{bmatrix}
\]
C) \[
\begin{bmatrix}
-\frac{5}{11} & -\frac{6}{11} \\
\frac{5}{11} & \frac{6}{11}
\end{bmatrix}
\]
D) Does not exist
Correct answer: ___
---
**Matrix Properties**
**20)** Which of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc702ff9-d3e6-4e4b-abbc-7bc2699ae04d%2F7e9920e8-05dd-4854-8478-11e594b3b592%2Fux3zlnf_processed.png&w=3840&q=75)
Transcribed Image Text:**Matrix Multiplication and Inverse Problems**
---
**Matrix Multiplication**
Find the matrix product mentally, without the use of a calculator or pencil-and-paper calculations.
**18)** Calculate the product of the matrices:
\[
\begin{bmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0 & 0 & 1
\end{bmatrix}
\]
and
\[
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{bmatrix}
\]
A) \[
\begin{bmatrix}
1 & 2 & 3 \\
4 & 5 & 6 \\
7 & 8 & 9
\end{bmatrix}
\]
B) \([1]\)
C) \[
\begin{bmatrix}
9 & 8 & 7 \\
6 & 5 & 4 \\
3 & 2 & 1
\end{bmatrix}
\]
D) \[
\begin{bmatrix}
1 & -2 & 3 \\
-4 & 5 & -6 \\
7 & -8 & 9
\end{bmatrix}
\]
Correct answer: ___
---
**Matrix Inverse**
Find the inverse, if it exists, of the given matrix:
**19)**
\[
\begin{bmatrix}
-6 & -6 \\
-5 & -5
\end{bmatrix}
\]
A) \[
\begin{bmatrix}
-\frac{5}{11} & \frac{6}{11} \\
\frac{5}{11} & -\frac{6}{11}
\end{bmatrix}
\]
B) \[
\begin{bmatrix}
\frac{5}{11} & -\frac{6}{11} \\
-\frac{5}{11} & \frac{6}{11}
\end{bmatrix}
\]
C) \[
\begin{bmatrix}
-\frac{5}{11} & -\frac{6}{11} \\
\frac{5}{11} & \frac{6}{11}
\end{bmatrix}
\]
D) Does not exist
Correct answer: ___
---
**Matrix Properties**
**20)** Which of
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