A is a 2 by 2 matrix with eigenvalues 175 and 315 Give the d

A is a 2 by 2 matrix with eigenvalues 1.75 and 3.15. Give the determinant of A. A is a 3 by 3 matrix with eigenvalues-1.2, 2.3 and 3.4. Give the determinant of A. A is a 3 by 3 matrix with eigenvalues -1.2, 2.3 and 3.4. Give the sum of the diagonal entries of A.

Solution

1) Determinant = product of all eigen values = 1.75*3.15 = 5.5125

2) Determinant = product of all eigen values = -1.2*2.3*3.4 = -9.384

3)  The sum of the main diagonal entries of A, called the trace of A, equals the sum of the eigenvalues of A.

So, sum of the main diagonal entries of A,= -1.2 +2.3 +3.4 = 4.5