Question

Find a matrix A such that 2A - 3B +5C =0
, where B=-2 2 0
3 1 4 and C= 2 0 -2
7 1 6​

Answer 1

The matrix $A = \left[\begin{array}{ccc}-8&3&5\\-13&-1&-9\end{array}\right]$.

Step-by-step explanation:

Given,

$B = \left[\begin{array}{ccc}-2&2&0\\3&1&4\end{array}\right]$

$C = \left[\begin{array}{ccc}2&0&-2\\7&1&6\end{array}\right]$

2A - 3B + 5C = 0

$=> 2A - 3\left[\begin{array}{ccc}-2&2&0\\3&1&4\end{array}\right] + 5\left[\begin{array}{ccc}2&0&-2\\7&1&6\end{array}\right]\\=> 2A - \left[\begin{array}{ccc}-6&6&0\\9&3&12\end{array}\right] +\left[\begin{array}{ccc}10&0&-10\\35&5&30\end{array}\right] \\=> 2A = \left[\begin{array}{ccc}-6&6&0\\9&3&12\end{array}\right] - \left[\begin{array}{ccc}10&0&-10\\35&5&30\end{array}\right]\\=> 2A = \left[\begin{array}{ccc}-6-10&6-0&0+10\\9-35&3-5&12-30\end{array}\right]$

$=>2A = \left[\begin{array}{ccc}-16&6&10\\-26&-2&-18\end{array}\right] \\=> A = \frac{1}{2}\left[\begin{array}{ccc}-16&6&10\\-26&-2&-18\end{array}\right]\\=> A = \left[\begin{array}{ccc}\frac{-16}{2}&\frac{6}{2}&\frac{10}{2}\\\frac{-26}{2}&\frac{-2}{2}&\frac{-18}{2}\end{array}\right]\\=> A = \left[\begin{array}{ccc}-8&3&5\\-13&-1&-9\end{array}\right]$

Hence, the matrix $A = \left[\begin{array}{ccc}-8&3&5\\-13&-1&-9\end{array}\right]$.

Answer 2

Answer:

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