Determine whether the mapping Tx A Ax is invertible where A

Determine whether the mapping T(x) A = Ax is invertible, where A = [0 3 -5 1 1 2 -5 -11 7].

Solution

A is the matrix representation of linear map T

mapping T is invertible if and only if the matrix A is invertible.

Matrix A is invertible if and only if its determinant is non zero. So we compute its determinant.

det(A)=-3(1*7-(-5*2))-5(1*(-11)-(-5*1))=-3(17)-5(-11+5)=-51-5(-6)=-51+30=-21

So the det(A) is non zero hence A is invertible and hence T is invertible

Matrix representation of T is the inverse of matrix A