Let -2 0 A= -3 1 Find A-, if it exists. 1 2 а) 3 1 2

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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# Matrix Inversion Problem

**Matrix Definition:**

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

**Problem Statement:**

Find \( A^{-1} \), if it exists.

**Answer Options:**

a)  
\[ 
\begin{bmatrix} 
-\frac{1}{2} & 0 \\ 
-\frac{3}{2} & 1 
\end{bmatrix} 
\]

b)  
\[ 
\begin{bmatrix} 
-\frac{3}{2} & 2 \\ 
-\frac{5}{2} & 3 
\end{bmatrix} 
\]

c)  
\( A \) does not have an inverse.

d)  
\[ 
\begin{bmatrix} 
-\frac{3}{2} & -1 \\ 
\frac{1}{2} & 3 
\end{bmatrix} 
\]

e)  
\[ 
\begin{bmatrix} 
\frac{3}{2} & -2 \\ 
\frac{1}{2} & 0 
\end{bmatrix} 
\]

f)  
None of the above.
Transcribed Image Text:# Matrix Inversion Problem **Matrix Definition:** Let \[ A = \begin{bmatrix} -2 & 0 \\ -3 & 1 \end{bmatrix} \] **Problem Statement:** Find \( A^{-1} \), if it exists. **Answer Options:** a) \[ \begin{bmatrix} -\frac{1}{2} & 0 \\ -\frac{3}{2} & 1 \end{bmatrix} \] b) \[ \begin{bmatrix} -\frac{3}{2} & 2 \\ -\frac{5}{2} & 3 \end{bmatrix} \] c) \( A \) does not have an inverse. d) \[ \begin{bmatrix} -\frac{3}{2} & -1 \\ \frac{1}{2} & 3 \end{bmatrix} \] e) \[ \begin{bmatrix} \frac{3}{2} & -2 \\ \frac{1}{2} & 0 \end{bmatrix} \] f) None of the above.
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