How do you find the inverse of #"A"=((5, 8), (17, 3))#?

1 Answer
Mar 1, 2016

Answer:

#"A"^-1=((-3/121,8/121),(17/121,-5/121))#

Explanation:

The inverse of the matrix

#"A"=((a,b),(c,d))#

is equal to

#"A"^-1=1/("det A")((d,-b),(-c,a))#

Note that #"det A"# is the determinant of #"A"# and is equal to #ad-bc#, so

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

For the matrix

#"A"=((5,8),(17,3))#

we have

#{(a=5),(b=8),(c=17),(d=3):}#

so

#"A"^-1=1/(5(3)-17(8))((3,-8),(-17,5))#

#"A"^-1=-1/121((3,-8),(-17,5))#

#"A"^-1=((-3/121,8/121),(17/121,-5/121))#