# Test: Matrices II - Ambitious

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Question 1:   Find $x$ and $y$: $\left[\begin{array}{cc}-2& 3\\ 4& -5\end{array}\right]\left[\begin{array}{cc}x& 2\\ 7& y\end{array}\right]=\left[\begin{array}{cc}23& 5\\ -13& -7\end{array}\right]$
$x=-2,y=-5$
$x=-1,y=3$
$x=-10.5,y=-1\frac{3}{4}$
$x=23,y=7$
Question 2:   Find $p$ and $q$: $\left[\begin{array}{cc}3& 5\\ 4& -1\end{array}\right]\left[\begin{array}{cc}p& 2\\ 2& q\end{array}\right]=\left[\begin{array}{cc}7& 31\\ -6& 3\end{array}\right]$
$p=3,q=-1$
$p=7,q=3$
$p=-1,q=5$
$p=4,q=2$
Question 3:   Find $\mathrm{det}A$ if $A=\left[\begin{array}{cc}5& 7\\ -6& -4\end{array}\right]$
$|A|=-20$
$|A|=17$
$|A|=22$
$|A|=62$
Question 4:   Which of the matrices is singular?
$B=\left[\begin{array}{cc}-7& 2\\ 7& 2\end{array}\right]$
$D=\left[\begin{array}{cc}3& 1\\ 1& 0\end{array}\right]$
$A=\left[\begin{array}{cc}-3& 6\\ -4& 8\end{array}\right]$
$C=\left[\begin{array}{cc}-5& 0\\ 0& 5\end{array}\right]$
Question 5:   Which of the following matrices is the transpose of $B$, if

$B=\left[\begin{array}{cccc}2& 3& -1& 1\\ 5& 0& 8& 3\\ -6& 5& 2& 5\\ 8& 7& 0& -1\end{array}\right]$?
${B}^{T}=\left[\begin{array}{cccc}2& 5& -6& 8\\ 3& 0& 5& 7\\ -1& 8& 2& 0\\ 1& 3& 5& -1\end{array}\right]$
${B}^{T}=\left[\begin{array}{cccc}8& 7& 0& -1\\ -6& 5& 2& 5\\ 5& 0& 8& 3\\ 2& 3& -1& 1\end{array}\right]$
${B}^{T}=\left[\begin{array}{cccc}1& -1& 3& 2\\ 3& 8& 0& 5\\ 5& 2& 5& -6\\ -1& 0& 7& 8\end{array}\right]$
${B}^{T}=\left[\begin{array}{cccc}1& 3& 5& -1\\ -1& 8& 2& 0\\ 3& 0& 5& 7\\ 2& 5& -6& 8\end{array}\right]$
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