If A = [(1 3), (2 4)], B = [(3 7), (8 2)] and 2x + A = B, find the value of x.
If A = [(1 3), (2 4)], B = [(3 7), (8 2)] and 2x + A = B, find the value of x.
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A = \(\begin{bmatrix}1&3\\2&4\end{bmatrix}\) B = \(\begin{bmatrix}3&7\\8&2\end{bmatrix}\)
2x + A = B ⇒ 2x = B - A ⇒ x = \(\frac12\)(B - A)
x = \(\frac12\)\(\left(\begin{bmatrix}3&7\\8&2\end{bmatrix}-\begin{bmatrix}1&3\\2&4\end{bmatrix}\right)\)
= \(\frac12\) \(\begin{bmatrix}2&4\\6&-2\end{bmatrix}\)
= \(\begin{bmatrix}1&2\\3&-1\end{bmatrix}\)
\(\therefore\) x = \(\begin{bmatrix}1&2\\3&-1\end{bmatrix}\)
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