# Invertible Matrices

• Oct 15th 2009, 03:31 PM
arizona11
Invertible Matrices
Suppose A=[a1 a2 a3] is an invertible 3x3 matrix satisfying:
A(1 2 1 )= (1 0 0) and A(-1 -1 2)=(1 1 0) (those are supposed to be columns not rows sorry)
(a) Determine the first column of A-1
(b)Determine the second column of A-1
hint: the transformations associated are linear.

If someone could please explain how to do this it would be greatly appreciated.
• Oct 15th 2009, 11:19 PM
aman_cc
Quote:

Originally Posted by arizona11
Suppose A=[a1 a2 a3] is an invertible 3x3 matrix satisfying:
A(1 2 1 )= (1 0 0) and A(-1 -1 2)=(1 1 0) (those are supposed to be columns not rows sorry)
(a) Determine the first column of A-1
(b)Determine the second column of A-1
hint: the transformations associated are linear.

If someone could please explain how to do this it would be greatly appreciated.

Refer to http://www.mathhelpforum.com/math-he...-w1-w2-w3.html

Note - A^-1 is itself a linear operator. And if A(x) = y => A^-1(y)=x