How do you find the inverse of [(9,13), (27,36)]?

3 Answers
Jul 22, 2017

A^(-1)=[(-4/3,13/27),(1,-1/3)]

Explanation:

Let's say A=[(9,13),(27,36)]

The inverse is then : A^(-1)=1/(det(A))adj(A)

1/(det(A))=1/(9*36-13*27)=-1/27

adj(A)=[(36,-13),(-27,9)]

So A^(-1)=-1/27[(36,-13),(-27,9)]=[(-36/27,13/27),(27/27,-9/27)]=

[(-4/3,13/27),(1,-1/3)]

Jul 22, 2017

The inverse is =-1/27((36,-13),(-27,9))

Explanation:

The inverse of the matrix A=((a,b),(c,d)) is

A^-1=1/(detA)*((d,-b),(-c,a))

Let A=((9,13),(27,36))

The determinant of A is

detA=|((9,13),(27,36))|=36*9-27*13=-27

As detA!=0, the matrix A is invertible

A^-1=-1/27((36,-13),(-27,9))

Verification

A*A^-1=((9,13),(27,36))*(-1/27)((36,-13),(-27,9))=((1,0),(0,1))

Jul 22, 2017

A^-1=((-4/3,13/27),(1,-1/3))

Explanation:

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

"then the inverse "A^-1" is"

A^-1=1/(detA)((d,-b),(-c,a))

detA=ad-bc

rArrdetA=(9xx36)-(13xx27)=-27

rArrA^-1=-1/27((36,-13),(-27,9))

color(white)(rAeeA^-1)=((-4/3,13/27),(1,-1/3))