Question

How do you find the inverse of `A=``((9, -5), (-7, 4))`?

Answer 1

`((4,5),(7,9))`

Explanation:

For a 2 x 2 matrix , the inverse may be found as follows:

If `A =( (a,b),(c,d))`

then the inverse matrix `A^-1 = 1/(ad-bc)((d,-b),(-c,a))`

ad-bc is the determinant of the matrix and it's value determines whether the matrix has an inverse or not
If (ad - bc ) = 0 then an inverse does not exist.

in this question a=9 , b=-5 , c = -7 and d=4

ad-bc `= (9 xx 4 ) -(-5 xx(-7)) = 36 - 35 = 1`
hence an inverse exists.

`A^-1 = ((4,5),(7,9))`

The inverse of a matrix may also be found using
`color(blue)" Gaussian Elimination "`
but is usually used in higher order matrices `3 xx 3 " and above"`