Question

What is the determinant of an elementary row replacement matrix?

An elementary n xn row replacement matrix is the same as the n x n identity matrix with__________ of the_____________replaced with some number k.This means this is the ___________and so its determinent is ___________.of its diagnol enteries. Thus, the determinant of an elementary row replacement matrix is______________.
1. Exactly one,atleast one
2. 1's or 0's
3. Identity matrix,invertible matrix, triangular matrix or zero matrix.
4. Product or sum
5. A number

Answer 1

Explanation:

Recall that an elementary matrix of a matrix operation is obtained by applying the matrix operation to the identity matrix. In this case, by replacement, it means changing the whole row of a matrix and replacing it with a the same row multiplied by a number k.

In this case, the solution is

What is the determinant of an elementary row replacement matrix?

An elementary n xn row replacement matrix is the same as the n x n identity matrix with Exactly one of the 1's replaced with some number k.This means this is the triangular matrix and so its determinent is product of its diagonal entries. Thus, the determinant of an elementary row replacement matrix is a number. Especifically, the number k we used to replace the one

1. Exactly one,atleast one

2. 1's or 0's

3. Identity matrix,invertible matrix, triangular matrix or zero matrix.

4. Product or sum

5. A number