模擬テスト6-1
[1]
次のうち計算できるものは計算し、計算できないものは計算不能と答えよ。
(1)
$(1,-2)\left(
\begin{array}{cc}
4 \\
3
\end{array}
\right)
$
(2)
$\left(
\begin{array}{cc}
0 \\
1
\end{array}
\right)
\left(
\begin{array}{cc}
2 & 1 \\
4 & 1
\end{array}
\right)
$
(3)
$\left(
\begin{array}{cc}
0 & -1 \\
1 & 0
\end{array}
\right)
\left(
\begin{array}{cc}
2 & 1 & 3 \\
2 & 5 & 9
\end{array}
\right)
$
(4)
$\left(
\begin{array}{cc}
0 & 0 \\
0 & 0
\end{array}
\right)
\left(
\begin{array}{cc}
-2 \\
22
\end{array}
\right)
$
(5)
$\left(
\begin{array}{cc}
2 & 5 & -3
\end{array}
\right)
\left(
\begin{array}{cc}
8 \\
-2 \\
2
\end{array}
\right)
$
(6)
$\left(
\begin{array}{cc}
3 & 1 \\
0 & 5 \\
-2 & 4
\end{array}
\right)
\left(
\begin{array}{cc}
-3 \\
2
\end{array}
\right)
$
(7)
$\left(
\begin{array}{cc}
1 & 2 & 0 \\
0 & -3 & 1\\
2 & 0 & -1
\end{array}
\right)
\left(
\begin{array}{cc}
-2 & 3 & 0 \\
0 & -1 & 2\\
1 & 0 & -1
\end{array}
\right)
$
(8)
$\left(
\begin{array}{cc}
4\\
3\\
1
\end{array}
\right)
\left(
\begin{array}{cc}
1 & -2 & 7
\end{array}
\right)
$
(9)
$\left(
\begin{array}{cc}
-1\\
0\\
5
\end{array}
\right)
\left(
\begin{array}{cc}
9 & -2 & 7 \\
1 & 0 & 3
\end{array}
\right)
$
(10)
$\left(
\begin{array}{cc}
0\\
7\\
-3
\end{array}
\right)
\left(
\begin{array}{cc}
4 & -8
\end{array}
\right)
$
[2]
(1)
$
A =\left(
\begin{array}{cc}
0 & -2 \\
1 & -1
\end{array}
\right),
B =\left(
\begin{array}{cc}
1 & 2 \\
3 & 4
\end{array}
\right)
$の時、$2(3A-2B)-(3A-8B)$の値を求めよ。
(2)
$
A =\left(
\begin{array}{cc}
5 & -1 \\
0 & 2
\end{array}
\right),
B =\left(
\begin{array}{cc}
1 & 2 \\
-3 & 1
\end{array}
\right)
$の時、$\displaystyle \frac{1}{2}\bigr(2A-B-X\bigl)=2\bigr(X-(2A-3B)\bigl)$を満たす行列Xを求めよ。
(3)
$
A =\left(
\begin{array}{cc}
a & 2 \\
b & 3
\end{array}
\right),
B =\left(
\begin{array}{cc}
2 & -1 \\
-2 & 1
\end{array}
\right)
$かつ$AB=0$の時、$a,b$の値を求めよ。
(4)
$
A =\left(
\begin{array}{cc}
a & 2 \\
b & 3
\end{array}
\right),
B =\left(
\begin{array}{cc}
2 & -1 \\
-2 & 1
\end{array}
\right)
$かつ$AB=BA$の時、$a,b$の値を求めよ。
(5)
$
A =\left(
\begin{array}{cc}
2 & 4\\
1 & -1
\end{array}
\right)
$の時、$A^3+A^2-3A-8E$を求めよ。
(6)
$
A =\left(
\begin{array}{cc}
1 & 2\\
0 & 1
\end{array}
\right)
$の時、$A^7-2A^6+A^5$を求めよ。
(7)
$
A =\left(
\begin{array}{cc}
a & b \\
-1 & 2
\end{array}
\right),
B =\left(
\begin{array}{cc}
1 & -1 \\
c & d
\end{array}
\right)
$について$A^{-1}=B$の時、$a,b,c,d$の値を求めよ。
(8)
$
A =\left(
\begin{array}{cc}
2 & 1 \\
5 & 3
\end{array}
\right),
B =\left(
\begin{array}{cc}
4 & 3 \\
3 & 2
\end{array}
\right)
$の時、$XA=B$を満たす行列$X$を求めよ。
(9)
$
A =\left(
\begin{array}{cc}
2 & 1 \\
5 & 3
\end{array}
\right),
B =\left(
\begin{array}{cc}
4 & 3 \\
3 & 2
\end{array}
\right)
$の時、$AX=B$を満たす行列$X$を求めよ。
(10)
$
A =\left(
\begin{array}{cc}
1 & 1 \\
a & b
\end{array}
\right)
$について、$A^2=0$の時、$a,b$の値を求めよ。