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What are the values of $(x, y, z, t)$, where
$3\left[\begin{array}{ll}x & y \\ z & t\end{array}\right]=\left[\begin{array}{cc}x & 6 \\ -1 & 2 t\end{array}\right]+\left[\begin{array}{cc}4 & x+y \\ z+t & 3\end{array}\right]=?$
Options:
$3\left[\begin{array}{ll}x & y \\ z & t\end{array}\right]=\left[\begin{array}{cc}x & 6 \\ -1 & 2 t\end{array}\right]+\left[\begin{array}{cc}4 & x+y \\ z+t & 3\end{array}\right]=?$
Solution:
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Verified Answer
The correct answer is:
$(2,4,1,3)$
$3\left[\begin{array}{ll}x & y \\ z & t\end{array}\right]=\left[\begin{array}{cc}x & 6 \\ -1 & 2 t\end{array}\right]+\left[\begin{array}{cc}4 & x+y \\ z+t & 3\end{array}\right]$
$\left[\begin{array}{cc}3 x & 3 y \\ 3 z & 3 t\end{array}\right]=\left[\begin{array}{cc}x+4 & 6+x+y \\ -1+z+t & 2 t+3\end{array}\right]$
On compairing two matrices are equal iff their corresponding elements are equal
$\therefore(x, y, z, t)=(2,4,1,3)$
$\left[\begin{array}{cc}3 x & 3 y \\ 3 z & 3 t\end{array}\right]=\left[\begin{array}{cc}x+4 & 6+x+y \\ -1+z+t & 2 t+3\end{array}\right]$
On compairing two matrices are equal iff their corresponding elements are equal
$\therefore(x, y, z, t)=(2,4,1,3)$
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