Question

PLZZZ HELP Find the inverse of a 2x2 matrix


Plz give answer .

Answer 1

`\left[\begin{array}{cc}-(1)/(2)&(1)/(6)\\-(1)/(2)&(1)/(3)\\\end{array}\right]`

Explanation:

If a 2x2 matrix is given as:

`\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right]`

The inverse is:

`(1)/(ad-bc)\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]`

Our matrix given is:

`\left[\begin{array}{cc}-4&2\\-6&6\\\end{array}\right]`

Using the formula, let's find the inverse:

`(1)/(ad-bc)\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]\\=(1)/((-4)(6)-(-6)(2))\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=(1)/(-12)\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\left[\begin{array}{cc}-(1)/(2)&(1)/(6)\\-(1)/(2)&(1)/(3)\\\end{array}\right]`