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

1 Answer
Feb 18, 2016

Answer:

#((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"#