(Solved): Can someone help me with this? Problem 4. (15 pts) Use the determinant to find out for which value ...

Can someone help me with this?

Problem 4. (15 pts) Use the determinant to find out for which value(s) of the constant k the 11 2 3 given matrix is invertible. 4 k 5 16 7 8 Problem 5. (10 pts) (a) Show that the eigenvalues , of a 2x2 matrix A are the solutions of the equation fa 22 - tr(A) 1 + (det A) = 0 (b ) Assume that A is an nxn orthogonal matrix, show that the possible real eigenvalues of A are 1 and -1. (hint: A is orthogonal if (and only if) ||Až || = || X || for all å in R”)