Jawaban Soal Latihan 1 Penjumlahan Dan Pengurangan Matriks

Soal Latihan 1

1. Diketahui matriks A, B dan C sebagai berikut :
   
   A = $\left(\left(,,\begin{array}{cc}-3& 2\\ 1& 3\end{array},,\right)\right)$
   
   B = $\left(\left(,,\begin{array}{cc}4& 1\\ 2& -5\end{array},,\right)\right)$
   
   C = $\left(\left(,,\begin{array}{cc}2& -2\\ 3& -1\end{array},,\right)\right)$
   
   Tentukan :
   1. A + B
   2. A - B
   3. B + C
   4. A - C
   5. C - B


2. Tentukan nilai x, y dan z dari persamaan matriks berikut :
   
   $\left(\left(,,\begin{array}{cc}\mathrm{x}& \mathrm{2y}\\ 8& \mathrm{3z}\end{array},,\right)\right)+\left(\left(,,\begin{array}{cc}5& 3\\ 1& 6\end{array},,\right)\right)=\left(\left(,,\begin{array}{cc}10& 11\\ 9& 15\end{array},,\right)\right)$
   
   


3. Diketahui matriks A dan B sebagai berikut :
   
   A = $\left(\left(,,\begin{array}{cc}6& \mathrm{z}\\ 10& \mathrm{x}\end{array},,\right)\right)$
   
   B = $\left(\left(,,\begin{array}{cc}\mathrm{2x}& \mathrm{2x}\\ 10& \frac{3}{2}\mathrm{y}\end{array},,\right)\right)$
   
   Tentukan nilai x, y dan z jika A - B = O

Jawab :

1. 1. A + B = $\left(\left(,,\begin{array}{cc}-3& 2\\ 1& 3\end{array},,\right)\right)+\left(\left(,,\begin{array}{cc}4& 1\\ 2& -5\end{array},,\right)\right)=\left(\left(,,\begin{array}{cc}1& 3\\ 3& -2\end{array},,\right)\right)$
      
   
   
   2. A - B = $\left(\left(,,\begin{array}{cc}-3& 2\\ 1& 3\end{array},,\right)\right)-\left(\left(,,\begin{array}{cc}4& 1\\ 2& -5\end{array},,\right)\right)=\left(\left(,,\begin{array}{cc}-7& 1\\ -1& 8\end{array},,\right)\right)$
      
      
   3. B + C = $\left(\left(,,\begin{array}{cc}4& 1\\ 2& -5\end{array},,\right)\right)+\left(\left(,,\begin{array}{cc}2& -2\\ 3& -1\end{array},,\right)\right)=\left(\left(,,\begin{array}{cc}6& -1\\ 5& -6\end{array},,\right)\right)$
      
      
   4. A - C = $\left(\left(,,\begin{array}{cc}-3& 2\\ 1& 3\end{array},,\right)\right)-\left(\left(,,\begin{array}{cc}2& -2\\ 3& -1\end{array},,\right)\right)=\left(\left(,,\begin{array}{cc}-5& 4\\ -2& 4\end{array},,\right)\right)$
      
      
   5. C - B = $\left(\left(,,\begin{array}{cc}2& -2\\ 3& -1\end{array},,\right)\right)-\left(\left(,,\begin{array}{cc}4& 1\\ 2& -5\end{array},,\right)\right)=\left(\left(,,\begin{array}{cc}-2& -3\\ 1& 4\end{array},,\right)\right)$
      
      


2. $\left(\left(,,\begin{array}{cc}\mathrm{x}& \mathrm{2y}\\ 8& \mathrm{3z}\end{array},,\right)\right)+\left(\left(,,\begin{array}{cc}5& 3\\ 1& 6\end{array},,\right)\right)=\left(\left(,,\begin{array}{cc}10& 11\\ 9& 15\end{array},,\right)\right)$
   
   x + 5 = 10
   x = 10 - 5
   x = 5
   
   2y + 3 = 11
   2y = 11 - 3
   2y = 8
   y = 4
   
   3z + 6 = 15
   3z = 15 - 6
   3z = 9
   z = 3


3. A - B = O
   
   $\left(\left(,,\begin{array}{cc}6& \mathrm{z}\\ 10& \mathrm{x}\end{array},,\right)\right)-\left(\left(,,\begin{array}{cc}\mathrm{2x}& \mathrm{2x}\\ 10& \frac{3}{2}\mathrm{y}\end{array},,\right)\right)=\left(\left(,,\begin{array}{cc}0& 0\\ 0& 0\end{array},,\right)\right)$
   
   6 - 2x = 0
   6 = 2x
   x = 3
   
   z - 2x = 0
   z - 2(3) = 0
   z = 6
   
   $\mathrm{x}-\frac{3}{2}\mathrm{y}=0$
   $3-\frac{3}{2}\mathrm{y}=0$
   $3=\frac{3}{2}\mathrm{y}$
   $\mathrm{y}=3.\frac{2}{3}$
   $\mathrm{y}=2$