How do you find the inverse of #A=##((8, 6), (7, 5))#?

1 Answer
Sep 6, 2016

Answer:

#A^-1=((-2 1/2, 3), (3 1/2, -4))#

Explanation:

For #A=((8, 6), (7, 5))#

To find the inverse of a 2x2 matrix: #" "X=((a, b), (c, d))#

  1. Find the determinant: #absX = ab-cd#
  2. Change the matrix to #((d, -b), (-c, a))#
  3. Divide by the determinant

#A^-1 = 1/absA ((5, -6), (-7, 8))#

#absA=8xx5-7xx6 = -2#

#A^-1 = 1/-2((5, -6), (-7, 8))#

#A^-1=((-2 1/2, 3), (3 1/2, -4))#