Question\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 \\ \hline & & & & & & & & & & & & \\ \hline \end{tabular}
Circle the correct answer 1) If $A=\left[\begin{array}{cc}2 & 1 \\ 0 & -3\end{array}\right]$ and $p(x)=x^{2}-3 x+1$, then $p(A)=$ a) $\left[\begin{array}{cc}-1 & 0 \\ 0 & 14\end{array}\right]$ b) $\left[\begin{array}{cc}-1 & -4 \\ 0 & 19\end{array}\right]$ c) $\left[\begin{array}{cc}2 & 1 \\ 0 & -3\end{array}\right]$ d) $\left|\begin{array}{cc}2 & 1 \\ 0 & -3\end{array}\right|$ e) $\left[\begin{array}{cc}1 & -3 \\ 0 & 16\end{array}\right]$ 2) Let $A=\left[\begin{array}{cc}3 & 0 \\ -1 & 2 \\ 1 & 1\end{array}\right], B=\left[\begin{array}{cc}1 & -1 \\ 0 & 2\end{array}\right], C=\left[\begin{array}{ccc}1 & -1 & 2 \\ 3 & 1 & 5\end{array}\right]$. Then $\left(A+C^{7}\right) B=$ a) $\left[\begin{array}{cc}4 & 2 \\ -2 & 8 \\ 3 & 9\end{array}\right]$ b) $\left[\begin{array}{cc}3 & 3 \\ -2 & 8 \\ 3 & 9\end{array}\right]$ c) $\left[\begin{array}{cc}2 & 4 \\ -2 & 8 \\ 3 & 9\end{array}\right]$ d) $\left[\begin{array}{cc}5 & 1 \\ -2 & 8 \\ 3 & 9\end{array}\right]$ e) $\left[\begin{array}{cc}4 & 2 \\ -2 & 8 \\ 3 & 9\end{array}\right]$ 3) The values of $a$ such that the matrix $A=\left[\begin{array}{ccc}2 & b+c & a-2 b+2 c \\ 0 & -5 & -2 \\ 3 & c-1 & 8\end{array}\right]$ is symmetric are a) $a=-9$ b) $a=11$ c) $a=-5$ d) $a=-1$ e) $a=7$ 4) If a matrix $A$ satisfies $A^{2}+A-I=0$, then $A^{-1}=$ a) $A-I$ b) $A+I$ c) $I-A$ d) $-I-A$ e) $A$ 5) If $A=\left[\begin{array}{cc}1 & -2 \\ 0 & 1\end{array}\right]$ and $B=\operatorname{tr}(A) \cdot A A^{T}$, then $\operatorname{det}(B)=$ a) 400 b) 36 c) 4 d) 1 e) 0 6) If $\left|\begin{array}{lll}a & b & c \\ d & e & f \\ g & h & i\end{array}\right|=-6$, then $\left|\begin{array}{ccc}a & b & c \\ d & e & f \\ g-4 d & h-4 e & i-4 f\end{array}\right|=$ $\begin{array}{ll}\text { a) } 24 & \text { b) }-24\end{array}$ b) -24 c) 30 d) -30 e) 4 7) The value of $a$ such that the system $-6 x-\left(a^{2}+15\right) y=0$ $x+(a+1) y=0$ has only the trivial solution is a) $a \neq 2$ b) $a=3$ c) $a \neq 3$ d) $\alpha=2$ e) $a=1$ Page 1 of 2