e1s2kat26

2021-02-11

Simplify
1)$\left[\begin{array}{cc}4& 5\end{array}\right]+\left[\begin{array}{cc}6& -4\end{array}\right]$
2)$\left[\begin{array}{cc}4& -1\\ 3& 3\\ -5& -4\end{array}\right]-\left[\begin{array}{cc}4& -2\\ 3& 6\\ -5& -6\end{array}\right]$
3)$\left[\begin{array}{cc}4& -1\\ 6& -3\end{array}\right]+\left[\begin{array}{cc}5& -6\\ 5& -5\end{array}\right]-\left[\begin{array}{cc}-2& 0\\ -2& -6\end{array}\right]$
Solve for x and y
$\left[\begin{array}{cc}-10& -4\\ x& -1\end{array}\right]+\left[\begin{array}{cc}-5& 8\\ y& -10\end{array}\right]=\left[\begin{array}{cc}-15& x\\ 16& -11\end{array}\right]$

SchepperJ

Step 1 To solve the given matrices. Step 2 Given that 1)$\left[\begin{array}{cc}4& 5\end{array}\right]+\left[\begin{array}{cc}6& -4\end{array}\right]$
$\left[\begin{array}{cc}4+6& 5-4\end{array}\right]$
$\left[\begin{array}{cc}10& 1\end{array}\right]$
$\therefore \left[\begin{array}{cc}4& 5\end{array}\right]+\left[\begin{array}{cc}6& -4\end{array}\right]=\left[\begin{array}{cc}10& 1\end{array}\right]$
2)$\left[\begin{array}{cc}4& -1\\ 3& 3\\ -5& -4\end{array}\right]-\left[\begin{array}{cc}4& -2\\ 3& 6\\ -5& -6\end{array}\right]$
$\left[\begin{array}{cc}4-4& -1+2\\ 3-3& 3-6\\ -5+5& -4+6\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& -3\\ 0& 2\end{array}\right]$
$\therefore \left[\begin{array}{cc}4& -1\\ 3& 3\\ -5& -4\end{array}\right]-\left[\begin{array}{cc}4& -2\\ 3& 6\\ -5& -6\end{array}\right]=\left[\begin{array}{cc}0& 1\\ 0& -3\\ 0& 2\end{array}\right]$
3)$\left[\begin{array}{cc}4& -1\\ 6& -3\end{array}\right]+\left[\begin{array}{cc}5& -6\\ 5& -5\end{array}\right]-\left[\begin{array}{cc}-2& 0\\ -2& -6\end{array}\right]$
$\left[\begin{array}{cc}4+5+2& -1-6-0\\ 6+5+2& -3-5+6\end{array}\right]$
$\left[\begin{array}{cc}3& -5\\ 13& -2\end{array}\right]$
$\therefore \left[\begin{array}{cc}4& -1\\ 6& -3\end{array}\right]+\left[\begin{array}{cc}5& -6\\ 5& -5\end{array}\right]-\left[\begin{array}{cc}-2& 0\\ -2& -6\end{array}\right]=\left[\begin{array}{cc}3& -5\\ 13& -2\end{array}\right]$
Given that
$\left[\begin{array}{cc}-10& -4\\ x& -1\end{array}\right]+\left[\begin{array}{cc}-5& 8\\ y& -10\end{array}\right]=\left[\begin{array}{cc}-15& x\\ 16& -11\end{array}\right]$
$\left[\begin{array}{cc}-10-5& -4+8\\ x+y& -1-10\end{array}\right]=\left[\begin{array}{cc}-15& x\\ 16& -11\end{array}\right]$
$\left[\begin{array}{cc}-15& 4\\ x+y& -11\end{array}\right]=\left[\begin{array}{cc}-15& x\\ 16& -11\end{array}\right]$
Equating on both sides we have
x=4
x+y=16
Since x=4 then 4+y=16
y=12

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