Question

Find matrix x which satisfies the equation given in attachment

Answer 1

Answer:

• $X=\left[\begin{array}{ccc}-1&-7\\-2&-1\\\end{array}\right]$

Step-by-step explanation:

$\pmb{\bf{\left[\begin{array}{ccc}3&6\\1&4\\\end{array}\right] }}+\pmb{\bf{\left[\begin{array}{ccc}0&2\\5&2\\\end{array}\right] }}+\bold{2X}=\pmb{\bf{\left[\begin{array}{ccc}1&-6\\2&4\\\end{array}\right] }}$

$\pmb{\bf{\left[\begin{array}{ccc}(3+0)&(6+2)\\(1+5)&(4+2)\\\end{array}\right] }}+\bold{2X}=\pmb{\bf{\left[\begin{array}{ccc}1&-6\\2&4\\\end{array}\right] }}$

$\pmb{\bf{\left[\begin{array}{ccc}3&8\\6&6\\\end{array}\right] }}+\bold{2X}=\pmb{\bf{\left[\begin{array}{ccc}1&-6\\2&4\\\end{array}\right] }}$

$\bold{2X}=\pmb{\bf{\left[\begin{array}{ccc}1&-6\\2&4\\\end{array}\right] }}-\pmb{\bf{\left[\begin{array}{ccc}3&8\\6&6\\\end{array}\right] }}$

$\bold{2X}=\pmb{\bf{\left[\begin{array}{ccc}(1-3)&(-6-8)\\(2-6)&(4-6)\\\end{array}\right] }}$

$\bold{2X}=\pmb{\bf{\left[\begin{array}{ccc}-2&-14\\-4&-2\\\end{array}\right] }}$

$\bold{X}=\pmb{\bf{\left[\begin{array}{ccc}\dfrac{-2}{2} &\dfrac{-14}{2} \\\dfrac{-4}{2} &\dfrac{-2}{2}\end{array}\right] }}$

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

Verification :

$\pmb{\bf{\left[\begin{array}{ccc}3&8\\6&6\\\end{array}\right] }}+\bold{2X}=\pmb{\bf{\left[\begin{array}{ccc}1&-6\\2&4\\\end{array}\right] }}$

$\pmb{\bf{\left[\begin{array}{ccc}3&8\\6&6\\\end{array}\right] }}\;$ $\;\bold{+}$  $\pmb{\bf{\left[\begin{array}{ccc}-2&-14\\-4&-2\\\end{array}\right] }}$ = $\pmb{\bf{\left[\begin{array}{ccc}1&-6\\2&4\\\end{array}\right] }}$

$\pmb{\bf{\left[\begin{array}{ccc}(3+(-2))&(8+(-14))\\6+(-4))&(6+(-2))\\\end{array}\right] }}$

$\pmb{\bf{\left[\begin{array}{ccc}1&-6\\2&4\\\end{array}\right] }}=\pmb{\bf{\left[\begin{array}{ccc}1&-6\\2&4\\\end{array}\right]}}$

∴ L.H.S = R.H.S