# Test: Matrices I - Ambitious

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Question 1:   Find $2A+3B$ for $A=\left[\begin{array}{cc}2& 3\\ 1& 5\end{array}\right]$and $B=\left[\begin{array}{cc}0& 4\\ 3& 1\end{array}\right]$
$\left[\begin{array}{cc}4& 12\\ 15& -4\end{array}\right]$
$\left[\begin{array}{cc}4& 17\\ 10& 21\end{array}\right]$
$\left[\begin{array}{cc}4& 18\\ 11& 13\end{array}\right]$
$\left[\begin{array}{cc}4& 16\\ 9& 19\end{array}\right]$
Question 2:   Find $\frac{1}{2}A-\frac{1}{3}B$ for $A=\left[\begin{array}{cc}4& 2\\ 6& 8\end{array}\right]$ and $B=\left[\begin{array}{cc}9& 15\\ 12& 6\end{array}\right]$
$\left[\begin{array}{cc}1& -3\\ -2& 4\end{array}\right]$
$\left[\begin{array}{cc}-2& -5\\ -3& 4\end{array}\right]$
$\left[\begin{array}{cc}2& -1\\ 4& -1\end{array}\right]$
$\left[\begin{array}{cc}-1& -4\\ -1& 2\end{array}\right]$
Question 3:   Find $2A-3B+4C$ for $A=\left[\begin{array}{cc}3& 5\\ -1& 4\end{array}\right]$, $B=\left[\begin{array}{cc}0& -5\\ 7& 8\end{array}\right]$ and $C=\left[\begin{array}{cc}-1& 2\\ -5& 3\end{array}\right]$
$\left[\begin{array}{cc}7& -23\\ 18& 5\end{array}\right]$
$\left[\begin{array}{cc}-11& 18\\ -34& 3\end{array}\right]$
$\left[\begin{array}{cc}3& 27\\ -23& 5\end{array}\right]$
$\left[\begin{array}{cc}2& 33\\ -43& -4\end{array}\right]$
Question 4:   Find ${A}^{2}$ for $A=\left[\begin{array}{cc}2& 1\\ 3& 4\end{array}\right]$
$\left[\begin{array}{cc}4& 1\\ 9& 16\end{array}\right]$
$\left[\begin{array}{cc}5& 3\\ 15& 16\end{array}\right]$
$\left[\begin{array}{cc}7& 6\\ 18& 19\end{array}\right]$
$\left[\begin{array}{cc}4& 1\\ 9& 16\end{array}\right]$
Question 5:   Find ${A}^{2}$ for $A=\left[\begin{array}{cc}-3& 5\\ 2& -4\end{array}\right]$
$\left[\begin{array}{cc}-6& 10\\ 4& -8\end{array}\right]$
$\left[\begin{array}{cc}9& 25\\ 4& 16\end{array}\right]$
$\left[\begin{array}{cc}19& -35\\ -14& 26\end{array}\right]$
$\left[\begin{array}{cc}16& -30\\ -12& 22\end{array}\right]$
Question 6:   Find $AB-BA$ , $A=\left[\begin{array}{cc}3& -1\\ 1& 4\end{array}\right]$, $B=\left[\begin{array}{cc}2& 5\\ -3& 6\end{array}\right]$
$\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$
$\left[\begin{array}{cc}-2& 27\\ -7& 2\end{array}\right]$
$\left[\begin{array}{cc}-5& 24\\ -10& -1\end{array}\right]$
$\left[\begin{array}{cc}1& 30\\ -4& 5\end{array}\right]$
Question 7:   Find $AB$ , $A=\left[\begin{array}{ccc}3& 1& 4\\ 0& -2& -1\end{array}\right]$, $B=\left[\begin{array}{c}2\\ -1\\ 3\end{array}\right]$
$\left[\begin{array}{c}17\\ -1\end{array}\right]$
$\left[\begin{array}{ccc}6& -1& 12\\ 0& 2& -3\end{array}\right]$
$\left[\begin{array}{ccc}6& 2& 8\end{array}\right]$
$\left[\begin{array}{c}12\\ 5\end{array}\right]$
Question 8:   Find $AB$ , $A=\left[\begin{array}{ccc}2& -3& 1\\ 1& 4& 2\end{array}\right]$, $B=\left[\begin{array}{cc}2& -1\\ -2& 4\\ 3& 7\end{array}\right]$
$\left[\begin{array}{cc}7& -1\\ 1& 34\end{array}\right]$
$\left[\begin{array}{cc}13& -7\\ 0& 29\end{array}\right]$
$\left[\begin{array}{cc}4& 3\\ -2& 16\end{array}\right]$
$\left[\begin{array}{cc}11& 8\\ 5& -4\end{array}\right]$
Question 9:   Solve: $\left[\begin{array}{cc}x& 5\\ 3& -1\end{array}\right]+\left[\begin{array}{cc}-1& -7\\ 2& 5\end{array}\right]-\left[\begin{array}{cc}-6& 2\\ 3& y\end{array}\right]=\left[\begin{array}{cc}12& -7\\ 18& 8\end{array}\right]$
$x=19,y=12$
$x=7,y=-4$
$x=-6,y=-1$
$x=12,y=8$
Question 10:   Solve: $\left[\begin{array}{cc}-2& 4\\ 3& 5\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}-5\\ 7\end{array}\right]$
$\left\{\begin{array}{l}x=2\frac{9}{22}\\ y=\frac{1}{22}\end{array}$
$\left\{\begin{array}{l}x=2\frac{7}{22}\\ y=-\frac{1}{22}\end{array}$
$\left\{\begin{array}{l}x=2\frac{13}{22}\\ y=-\frac{1}{22}\end{array}$
$\left\{\begin{array}{l}x=2\frac{37}{66}\\ y=-\frac{1}{22}\end{array}$