Question

question is from matrices


plz don't write inappropriate answers if dont know then leave ​

Answer 1

Solution:-

Given

$\to\tt \: A=\left[\begin{array}{cc} 2 & 1\\ 0 & - 2\end{array}\right]$

$\to\tt B=\left[\begin{array}{cc} 4 & 1\\ - 3 & - 2\end{array}\right]$

$\to \tt \: C =\left[\begin{array}{cc} - 3 & 2\\ - 1 & 4\end{array}\right]$

To find The value

$\to \tt \: A ^{2} + AC - 5B$

We can write as

$\to \tt \: A \times A + AC - 5B$

Now put the value

$\tt \to \left[\begin{array}{cc} 2 & 1\\ 0 & - 2\end{array}\right] \times \left[\begin{array}{cc} 2 & 1\\ 0 & - 2\end{array}\right] + \left[\begin{array}{cc} 2 & 1\\ 0 & - 2\end{array}\right] \times \tt \left[\begin{array}{cc} - 3 & 2\\ - 1 & 4\end{array}\right] + 5 \times \tt \left[\begin{array}{cc} 4 & 1\\ - 3 & - 2\end{array}\right]$

$\to \tt \: \left[\begin{array}{cc} 4 & 1\\ 0& 4\end{array}\right] + \left[\begin{array}{cc} - 6 & 2\\ 0& - 8\end{array}\right] + \tt \left[\begin{array}{cc} 20 & 5\\ - 15& - 10\end{array}\right]$

$\tt \to \: \tt \: \left[\begin{array}{cc} - 2 & 3\\ 0 & - 4\end{array}\right] - \tt \left[\begin{array}{cc} 20 & 5\\ - 15& - 10\end{array}\right]$

$\tt \to \: \left[\begin{array}{cc} -22 & -2\\ 15& 6\end{array}\right]$

Answer is

$\tt \to \: \left[\begin{array}{cc} -22 & -2\\ 15& 6\end{array}\right]$