How do you find the inverse of #[(6,-10), (-4,-5)]#?

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Answer 1 · 2017-02-19T10:21:17

The inverse matrix is #=((1/14,-1/7),(-2/35,-3/35))#

Let #A=((6,-10),(-4,-5))#

To determine if matrix #A# is invertible, we calculate the determinant

#detA=|(6,-10),(-4,-5)|=-6*5-(-10)(-4)=-30-40=-70#

As, #detA!=0#, the matrix is invertible

We start, by calculating the matrix of co-factors

#C=((-5,4),(10,6))#

Then, we calculate the transpose of matrix #C#

#C^T=((-5,10),(4,6))#

And the inverse is

#A^-1=1/detA*C^T#

#=-1/70*((-5,10),(4,6))#

#=((1/14,-1/7),(-2/35,-3/35))#

Verification,

#A*A^-1=((6,-10),(-4,-5))*((1/14,-1/7),(-2/35,-3/35))#

#=((1,0),(0,1))#

#=I#