Question

I want a solution with detailed explanation please!​

Answer 1

Solution:-

Given

$\rm \to \: A = \left[\begin{array}{cc}9&1\\4&3\end{array}\right]$

$\rm \to \: B = \left[\begin{array}{cc}1&5\\6&11\end{array}\right]$

To find

$\rm \to martix \: X \: such \: that \: 3 A + 5B + 2X = 0$

Now take :- 3A + 5B + 2X = 0 And put the value of A and B

$\rm \to \: 3\left[\begin{array}{cc}9&1\\4&3\end{array}\right] + 5\left[\begin{array}{cc}1&5\\6&11\end{array}\right] + 2X = 0$

$\rm \to\left[\begin{array}{cc}27&3\\12&9\end{array}\right] + \left[\begin{array}{cc}5&25\\30&55\end{array}\right] + 2X = 0$

$\rm \to\left[\begin{array}{cc}32&28\\42&64\end{array}\right] + 2X = 0$

$\rm \to2X = - \left[\begin{array}{cc}32&28\\42&64\end{array}\right]$

$\rm \to \: X = - \frac{1}{2} \left[\begin{array}{cc}32&28\\42&64\end{array}\right]$

$\rm \to \: X = - \left[\begin{array}{cc}16&14\\21&32\end{array}\right]$

Answer

$\rm \to \: X = - \left[\begin{array}{cc}16&14\\21&32\end{array}\right]$