Question 1

$$\text { Let } A = \left[ \begin{array} { r r } 
3 & - 2 \
2 & 1
\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 
- 1 & 2 \
6 & - 1
\end{array} \right]$$ Does the matrix A + B have an inverse?
A) Yes
B) No

Accepted Answer

The answer of \[\text { Let } A = \left[...

Question 2

Does a square matrix with a row of all zeros have an inverse?
A) Yes
B) No

Accepted Answer

A square matrix with a row of all zeros cannot have an inverse because its determinant is zero, indicating that it is singular or non-invertible.

Question 3

Provide an appropriate response.
-Let $\mathrm { P }$ be a $3 \times 3$ matrix that has a multiplicative inverse. Which of the following statements are false? (Let 0 represent the $3 \times 3$ zero matrix.)
(i) $0 \cdot \mathrm { P } = 0$
(ii) $\mathrm { PP } - 1 = 0$
(iii) $\mathrm { P } ^ { - 1 } \mathrm { P } = \mathrm { I } _ { 3 }$
(iv) $\mathrm { PP } ^ { - 1 } = \mathrm { P }$
A) (i), (iii)
B) (iv)
C) (ii)
D) (ii), (iv)

Accepted Answer

The answer of Provide an appropriate response.
-Let \(\mathrm { P...

Question 4

Let $A = \left[ \begin{array} { l l } 
e & 0 \
0 & a
\end{array} \right]$ where e and a are nonzero constants. Find $\mathrm { A } ^ { - 1 }$
A) $\left[ \begin{array} { c } 
\frac { 1 } { e } {1} \
1 \frac { 1 } { a }
\end{array} \right]$
B) $\left[ \begin{array} { l l } 
0 & e \
a & 0
\end{array} \right]$
C) $\left[ \begin{array} { l l } 
e & 0 \
0 & a
\end{array} \right]$
D)

Accepted Answer

The answer of Let \(A = \left[ \begin{array} { l...

Question 5

$$\text { Let } A = \left[ \begin{array} { r r } 
1 & - 4 \
4 & 6
\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 
1 & - 4 \
4 & 6
\end{array} \right]$$ Does the matrix A - B have an inverse?
A) Yes
B) No

Accepted Answer

The matrix $A - B$ results in a zero matrix since $A$ and $B$ are identical. The zero matrix does not have an inverse because its determinant is 0, and a matrix has an inverse only if its determinant is non-zero.

Quiz 6: Systems and Matrices

$\text { Let } A = \left[ \begin{array} { r r } 3 & - 2 \\2 & 1\end{array} \right] \text { and } B = \left[ \begin{array} { r r } - 1 & 2 \\6 & - 1\end{array} \right]$ Does the matrix A + B have an inverse?

Does a square matrix with a row of all zeros have an inverse?

Let $A = \left[ \begin{array} { l l } e & 0 \\0 & a\end{array} \right]$ where e and a are nonzero constants. Find $\mathrm { A } ^ { - 1 }$

$\text { Let } A = \left[ \begin{array} { r r } 1 & - 4 \\4 & 6\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 1 & - 4 \\4 & 6\end{array} \right]$ Does the matrix A - B have an inverse?

Quiz 6: Systems and Matrices

Let A=[3−221] and B=[−126−1]\text { Let } A = \left[ \begin{array} { r r } 3 & - 2 \\2 & 1\end{array} \right] \text { and } B = \left[ \begin{array} { r r } - 1 & 2 \\6 & - 1\end{array} \right] Let A=[32​−21​] and B=[−16​2−1​] Does the matrix A + B have an inverse?

Does a square matrix with a row of all zeros have an inverse?

Let A=[e00a]A = \left[ \begin{array} { l l } e & 0 \\0 & a\end{array} \right]A=[e0​0a​] where e and a are nonzero constants. Find A−1\mathrm { A } ^ { - 1 }A−1

Let A=[1−446] and B=[1−446]\text { Let } A = \left[ \begin{array} { r r } 1 & - 4 \\4 & 6\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 1 & - 4 \\4 & 6\end{array} \right] Let A=[14​−46​] and B=[14​−46​] Does the matrix A - B have an inverse?

$\text { Let } A = \left[ \begin{array} { r r } 3 & - 2 \\2 & 1\end{array} \right] \text { and } B = \left[ \begin{array} { r r } - 1 & 2 \\6 & - 1\end{array} \right]$ Does the matrix A + B have an inverse?

Let $A = \left[ \begin{array} { l l } e & 0 \\0 & a\end{array} \right]$ where e and a are nonzero constants. Find $\mathrm { A } ^ { - 1 }$

$\text { Let } A = \left[ \begin{array} { r r } 1 & - 4 \\4 & 6\end{array} \right] \text { and } B = \left[ \begin{array} { r r } 1 & - 4 \\4 & 6\end{array} \right]$ Does the matrix A - B have an inverse?