Question

[tex] Find a 2*2 matrix X such that \left[\begin{array}{ccc}5&-7\\-2&3\end{array}\right] X= \left[\begin{array}{ccc}-16&-6\\7&2\end{array}\right] [\tex]

Answer 1

Answer:

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

Step-by-step explanation:

$\left[\begin{array}{ccc}5&-7\\-2&3\\\end{array}\right] \left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]=\left[\begin{array}{ccc}-16&-6\\7&2\\\end{array}\right]$

$\textrm{equating both the sides we get,}$

5a-7c=-16

5b-7d=-6

-2a+3c=7

-2b+3d=2

$\textrm{on solving for a,b,c,d we get a=1;b=-4;c=3;d=-2}$

$\textrm{hence required matrix is}\left[\begin{array}{ccc}1&-4\\3&-2\\\end{array}\right]$

Answer 2

Answer:

$\left[\begin{array}{ccc}5&-7\\-2&3\end{array}\right] X= \left[\begin{array}{ccc}-16&-6\\7&2\end{array}\right]$

Step-by-step explanation:

$Multiply \: both \: sides \: of \: the \: \\ equation \: by \: \left(\begin{array}{cc}5 & -7 \\ -2 & 3\end{array}\right)-1 f \: \\ rom \: the \: left \: \[ A X=B \quad \Rightarrow \quad X=A^{-1} B$

$\mathtt{X=\left(\begin{array}{cc}5 & -7 \\ -2 & 3\end{array}\right)-1 \cdot\left(\begin{array}{cc}-16 & -6 \\ 7 & 2\end{array}\right)}$

$\mathtt{x=\left(\begin{array}{ll}1 & -4 \\ 3 & -2\end{array}\right)}$

hope it help you.