- I have a 3 x 3 matrix [a+8,1,0;1,a+2,6;0,6,1] with two unknown variables. I have to use Sylvester's criterion to find set values of parameter a where the matrix is positive definite.
What I thought to do is to find the determinant of the matrix and a would be the boundaries between the two values?
- Letting a = -2, the matrix is [6,1,0;1,0,6;0,6,1] which is indefinite. Without finding the eigenvectors, I have to find vector x such that x^t Ax > 0 and vector y y^t Ay<0
What I thought is that you make a 1 x 3 matrix for both x and y then mutliply with A. From that you calculate for det < 0 and det >0
Would this be the correct way of thinking for this question