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

3 Answers
Jul 22, 2017

Answer:

#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

Answer:

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

Answer:

#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))#