How do you find the inverse of #((7, -4),(-5, 3))#?

1 Answer
Feb 28, 2016

Answer:

#((3,4),(5,7))#

Explanation:

For a 2X2 matrix A , the inverse is found as follows:

For a matrix A = #((a,b),(c,d))#

Then the inverse #A^-1 = 1/(ad-bc)((d,-b),(-c,a))#

(ad - bc) is the determinant of the matrix , and if equal to zero, then the matrix has no inverse and is said to be singular.

here a = 7 b = -4 , c = -5 and d = 3

ad - bc =#(7xx3) - (-4xx-5) = 21 -20 = 1 #

hence an inverse matrix exists

#rArr A^-1 =( (3,4),(5,7))#