Linear Algebra and Determinant

[Swati]

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]

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]

what is U(0,1) ?
Please explain me, i couldn't understand.

 

[CaptainBlack]

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