Question

10. Optional Question. What would be the most efficient way to compute the determinant of an n by n matrix where n is large? Assume the matrix entries are all non-zero so you cannot take advantage of sparsity. Briefly explain why the method you suggest would be much more efficient than cofactor expansion. Hints: Recall that in general for an n by n matrix cofactor expansion to compute the determinant requires $n!$ operations. Also recall that the if a matrix is upper triangular, you can compute the determinant as the product of the diagonal elements. In addition, recall that row reduction to echlon form does not change the value of the determinant. (Assume no row interchanges or scaling is used.)

          10. Optional Question. What would be the most efficient way to compute the determinant of an n by n matrix where n is large? Assume the matrix entries are all non-zero so you cannot take advantage of sparsity. Briefly explain why the method you suggest would be much more efficient than cofactor expansion.
Hints: Recall that in general for an n by n matrix cofactor expansion to compute the determinant requires $n!$ operations. Also recall that the if a matrix is upper triangular, you can compute the determinant as the product of the diagonal elements. In addition, recall that row reduction to echlon form does not change the value of the determinant. (Assume no row interchanges or scaling is used.)

10. Optional Question. What would be the most efficient way to compute the determinant of an n by n matrix where n is large? Assume the matrix entries are all non-zero so you cannot take advantage of sparsity. Briefly explain why the method you suggest would be much more efficient than cofactor expansion.
Hints: Recall that in general for an n by n matrix cofactor expansion to compute the determinant requires n! operations. Also recall that the if a matrix is upper triangular, you can compute the determinant as the product of the diagonal elements. In addition, recall that row reduction to echlon form does not change the value of the determinant. (Assume no row interchanges or scaling is used.)

Added by Matthew M.

Question

Please give Ace some feedback