8.1 Operations of matrices (inverse)

1. Question

If [math]\begin{bmatrix}-1&7\\24&10\end{bmatrix}^{-1}=\dfrac{1}{p}\begin{bmatrix}a&b\\c&d\end{bmatrix}[/math] where [math]a, b, c, d[/math], and [math]p[/math] are integers, what is the value of [math]p[/math]?

2. Question

If [math]\begin{bmatrix}1&3\\2&7\end{bmatrix}^{-1}=\begin{bmatrix}a&b\\c&d\end{bmatrix}[/math] what are [math]a, b, c[/math], and [math]d[/math]?

[math]a=[/math] , [math]b=[/math]
[math]c=[/math] , [math]d=[/math]

3. Question

If [math]\begin{bmatrix}2&1\\5&3\end{bmatrix}^{-1}=\begin{bmatrix}a&b\\c&d\end{bmatrix}[/math] what are [math]a, b, c[/math], and [math]d[/math]?

[math]a=[/math] , [math]b=[/math]
[math]c=[/math] , [math]d=[/math]

4. Question

If [math]A[/math] be an invertible matrix, which of the following matrices is equivalent to [math](AMA^{-1})^{n}[/math] where [math]n[/math] is a positive integer?

[math]A^nM^n(A^{-1})^n[/math]
[math]M^n[/math]
[math]AM^nA^{-1}[/math]
None of the above

5. Question

If [math]\begin{bmatrix}2&7\\1&4\end{bmatrix}^{-1}=\begin{bmatrix}a&b\\c&d\end{bmatrix}[/math], what are [math]a, b, c[/math], and [math]d[/math]?

[math]a=[/math] , [math]b=[/math]
[math]c=[/math] , [math]d=[/math]

6. Question

Solve the matrix equation [math]\begin{bmatrix}2&0\\1&7\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}42\\-28\end{bmatrix}[/math]

[math]x=[/math]
[math]y=[/math]