Solve the equation for x,y,z and t if 2\(\begin{bmatrix}x&y\\y&t\end{bmatrix}\)+3\(\begin{bmatrix}1&-1\\0&2\end{bmatrix}\)=3\(\begin{bmatrix}3&5\\4&6\end{bmatrix}\)
Solve the equation for x,y,z and t if 2\(\begin{bmatrix}x&y\\y&t\end{bmatrix}\)+3\(\begin{bmatrix}1&-1\\0&2\end{bmatrix}\)=3\(\begin{bmatrix}3&5\\4&6\end{bmatrix}\)
Solution and Explanation
2\(\begin{bmatrix}x&y\\y&t\end{bmatrix}\)+3\(\begin{bmatrix}1&-1\\0&2\end{bmatrix}\)=3\(\begin{bmatrix}3&5\\4&6\end{bmatrix}\)
\(\Rightarrow \) \(\begin{bmatrix}2x&2z\\2y&2t\end{bmatrix}\)+\(\begin{bmatrix}3&-3\\0&6\end{bmatrix}\)=\(\begin{bmatrix}9&15\\12&18\end{bmatrix}\)
\(\Rightarrow \begin{bmatrix}2x+3&2z-3\\2y&2t+6\end{bmatrix}\)=\(\begin{bmatrix}9&15\\12&18\end{bmatrix}\)
Comparing the corresponding elements of these two matrices, we get:
2x+3=9
\(\Rightarrow\) x=3
2y=12
\(\Rightarrow\) y=6
2z-3=15
\(\Rightarrow\) 2z=18
z=9
2t+6=18
2t=12
t=6.
\(\therefore\) x=3,y=6,z=9 and t=6
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