Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter11: Systems Of Equations
Section11.3: Matrix Approa To Solving Linear Systems
Problem 51PS
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F1.5 question 23 on paper please
![### Educational Content on Matrix Operations
#### Graphical and Diagram Elements
This section contains several matrices that will be referenced in various exercises. Each matrix represents a collection of numbers arranged in a rectangular array of rows and columns. Below are the detailed exercises and their corresponding matrices.
#### Exercises
**Exercise 20**
- Part a:
\[
\begin{bmatrix}
0 & 0 & 0 & k_4 \\
0 & 0 & k_3 & 0 \\
0 & k_2 & 0 & 0 \\
k_1 & 0 & 0 & 0
\end{bmatrix}
\]
- Part b:
\[
\begin{bmatrix}
k & 0 & 0 & 0 \\
0 & k & 0 & 0 \\
0 & 0 & 1 & k \\
0 & 0 & k & 1
\end{bmatrix}
\]
**Exercise 21-22:**
Find all values of \( c \), if any, for which the given matrix is invertible.
1. Exercise 21:
\[
\begin{bmatrix}
c & c & c \\
1 & 1 & c \\
1 & 1 & c
\end{bmatrix}
\]
2. Exercise 22:
\[
\begin{bmatrix}
c & 1 & 0 \\
1 & c & 1 \\
0 & 1 & c
\end{bmatrix}
\]
**Exercise 23-26:**
Express the matrix and its inverse as products of elementary matrices.
1. Exercise 23:
\[
\begin{bmatrix}
-3 & 1 \\
2 & 2
\end{bmatrix}
\]
2. Exercise 24:
\[
\begin{bmatrix}
1 & 0 \\
-5 & 2
\end{bmatrix}
\]
3. Exercise 25:
\[
\begin{bmatrix}
0 & 4 & 3 \\
0 & 2 & 1
\end{b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fccdd90b5-cd41-4340-8a36-15b102c9ba73%2Fc883a184-80fa-4296-80d2-1d988eb1bab1%2Frwq2lh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content on Matrix Operations
#### Graphical and Diagram Elements
This section contains several matrices that will be referenced in various exercises. Each matrix represents a collection of numbers arranged in a rectangular array of rows and columns. Below are the detailed exercises and their corresponding matrices.
#### Exercises
**Exercise 20**
- Part a:
\[
\begin{bmatrix}
0 & 0 & 0 & k_4 \\
0 & 0 & k_3 & 0 \\
0 & k_2 & 0 & 0 \\
k_1 & 0 & 0 & 0
\end{bmatrix}
\]
- Part b:
\[
\begin{bmatrix}
k & 0 & 0 & 0 \\
0 & k & 0 & 0 \\
0 & 0 & 1 & k \\
0 & 0 & k & 1
\end{bmatrix}
\]
**Exercise 21-22:**
Find all values of \( c \), if any, for which the given matrix is invertible.
1. Exercise 21:
\[
\begin{bmatrix}
c & c & c \\
1 & 1 & c \\
1 & 1 & c
\end{bmatrix}
\]
2. Exercise 22:
\[
\begin{bmatrix}
c & 1 & 0 \\
1 & c & 1 \\
0 & 1 & c
\end{bmatrix}
\]
**Exercise 23-26:**
Express the matrix and its inverse as products of elementary matrices.
1. Exercise 23:
\[
\begin{bmatrix}
-3 & 1 \\
2 & 2
\end{bmatrix}
\]
2. Exercise 24:
\[
\begin{bmatrix}
1 & 0 \\
-5 & 2
\end{bmatrix}
\]
3. Exercise 25:
\[
\begin{bmatrix}
0 & 4 & 3 \\
0 & 2 & 1
\end{b
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