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Linear Algebra and Determinant

Swati

New member
Oct 30, 2012
16
1(a) Construct a 4*4 matrix whose determinant is easy to compute using cofactor expansion but hard to evaluate using elementary row operations.

(b) Construct a 4*4 matrix whose determinant is easy to compute using elementary row operations but hard to evaluate using cofactor expansion
 

CaptainBlack

Well-known member
Jan 26, 2012
890
1(a) Construct a 4*4 matrix whose determinant is easy to compute using cofactor expansion but hard to evaluate using elementary row operations.
Would a matrix with all elements zero except for those on the diagonal which are a random sample of size 4 from U(0,1) qualify?

(b) Construct a 4*4 matrix whose determinant is easy to compute using elementary row operations but hard to evaluate using cofactor expansion
Would a matrix with two rows equal but with values samples from U(0,1), and all other values sampled independently from U(0,1) qualify?

CB
 

Swati

New member
Oct 30, 2012
16
what is U(0,1) ?
Please explain me, i couldn't understand.
 

CaptainBlack

Well-known member
Jan 26, 2012
890
what is U(0,1) ?
Please explain me, i couldn't understand.
U(0,1) - the uniform distribution on [0,1). The suggestion is to use a random matrix generated in the specified way. In one case it would be diagonal, so the co-factor method would give the determinant as the product of the diagonal elements, in the second case with two equal rows row operations would deduce it has zero determinant.

CB