画像に示された行列計算の問題を解きます。問題は全部で9問あります。それぞれの計算結果を求めます。

1. 問題の内容

画像に示された行列計算の問題を解きます。問題は全部で9問あります。それぞれの計算結果を求めます。

2. 解き方の手順

(9) $(3-2)\left(\begin{array}{l}4 \\ 1\end{array}\right)$

$=(1)\left(\begin{array}{l}4 \\ 1\end{array}\right)=\left(\begin{array}{l}4 \\ 1\end{array}\right)$

(10) $\left(\begin{array}{l}2 \\ 4\end{array}\right)(-1 \quad 3)$

$=\left(\begin{array}{cc}-2 & 6 \\ -4 & 12\end{array}\right)$

(11) $\left(\begin{array}{l}2 \\ 4\end{array}\right)\left(\begin{array}{lll}2 & 1 & 0\end{array}\right)$

$=\left(\begin{array}{ccc}4 & 2 & 0 \\ 8 & 4 & 0\end{array}\right)$

(12) $\left(\begin{array}{lll}2 & -1 & 3\end{array}\right)\left(\begin{array}{c}3 \\ 2 \\ -3\end{array}\right)$

$=2(3)+(-1)(2)+3(-3)=6-2-9=-5$

(13) $\left(\begin{array}{c}3 \\ 0 \\ -1\end{array}\right)\left(\begin{array}{lll}1 & 2 & 3\end{array}\right)$

$=\left(\begin{array}{ccc}3 & 6 & 9 \\ 0 & 0 & 0 \\ -1 & -2 & -3\end{array}\right)$

(14) $\left(\begin{array}{c}3 \\ 0 \\ -1\end{array}\right)\left(\begin{array}{ll}1 & -3\end{array}\right)$

$=\left(\begin{array}{cc}3 & -9 \\ 0 & 0 \\ -1 & 3\end{array}\right)$

(15) $\left(\begin{array}{ccc}2 & -1 & 1 \\ 3 & 0 & 1\end{array}\right)\left(\begin{array}{c}3 \\ 0 \\ -1\end{array}\right)$

$=\left(\begin{array}{l}2(3)-1(0)+1(-1) \\ 3(3)+0(0)+1(-1)\end{array}\right)=\left(\begin{array}{l}6-0-1 \\ 9+0-1\end{array}\right)=\left(\begin{array}{l}5 \\ 8\end{array}\right)$

(16) $\left(\begin{array}{ccc}2 & -1 & 1 \\ 3 & 0 & 1\end{array}\right)\left(\begin{array}{cc}1 & 0 \\ 0 & 2 \\ -1 & -1\end{array}\right)$

$=\left(\begin{array}{ll}2(1)-1(0)+1(-1) & 2(0)-1(2)+1(-1) \\ 3(1)+0(0)+1(-1) & 3(0)+0(2)+1(-1)\end{array}\right)=\left(\begin{array}{cc}2-0-1 & 0-2-1 \\ 3+0-1 & 0+0-1\end{array}\right)=\left(\begin{array}{cc}1 & -3 \\ 2 & -1\end{array}\right)$

(17) $\left(\begin{array}{cc}1 & 0 \\ 0 & 2 \\ -1 & 1\end{array}\right)\left(\begin{array}{lll}2 & -1 & 1 \\ 3 & 0 & 1\end{array}\right)$

$=\left(\begin{array}{ccc}1(2)+0(3) & 1(-1)+0(0) & 1(1)+0(1) \\ 0(2)+2(3) & 0(-1)+2(0) & 0(1)+2(1) \\ -1(2)+1(3) & -1(-1)+1(0) & -1(1)+1(1)\end{array}\right)=\left(\begin{array}{ccc}2 & -1 & 1 \\ 6 & 0 & 2 \\ 1 & 1 & 0\end{array}\right)$

3. 最終的な答え

(9) $\left(\begin{array}{l}4 \\ 1\end{array}\right)$

(10) $\left(\begin{array}{cc}-2 & 6 \\ -4 & 12\end{array}\right)$

(11) $\left(\begin{array}{lll}4 & 2 & 0 \\ 8 & 4 & 0\end{array}\right)$

(12) $-5$

(13) $\left(\begin{array}{ccc}3 & 6 & 9 \\ 0 & 0 & 0 \\ -1 & -2 & -3\end{array}\right)$

(14) $\left(\begin{array}{cc}3 & -9 \\ 0 & 0 \\ -1 & 3\end{array}\right)$

(15) $\left(\begin{array}{l}5 \\ 8\end{array}\right)$

(16) $\left(\begin{array}{cc}1 & -3 \\ 2 & -1\end{array}\right)$

(17) $\left(\begin{array}{ccc}2 & -1 & 1 \\ 6 & 0 & 2 \\ 1 & 1 & 0\end{array}\right)$