A is a 4 by 4 matrix with eigenvalues 32 53 76 147 Givethe

A is a 4 by 4 matrix with eigenvalues - 3/2, 5/3, 7/6, 14/7. Givethe smallest eigenvalue of A^-1. A is a 4 by 4 matrix with eigenvalues - 3/2, 5/3, 7/6, 14/7 Give the smallest eigenvalue of A^T.

Solution

Property of eigen values:Suppose A is a square nonsingular matrix and is an eigenvalue of A. Then ^1 is an eigenvalue of the matrix A^1.

So, the eigen value for A = -3/2 would become -2/3 which is the eigen value of A^-1

Smalest eigen value ofA^-1 = -2/3

Property: Suppose A is a square matrix and is an eigenvalue of A. Then is an eigenvalue of the matrix At.

Smallest eigen value for At = -3/2

So, for A^t , smallest eigen value would be = -3/2