Question

for the given matrix, identify the Sequence of elementary matrices E1 ,E 2,…,E . . that transforms the matrix into echelon form.

Answer 1

To transform a matrix into echelon form, use elementary row operations and perform the same row operations on the identity matrix. Each row operation can be represented by an elementary matrix.

Step-by-step explanation:

To transform a matrix into echelon form, we can use elementary row operations. The sequence of elementary matrices required to transform a given matrix into echelon form can be determined by performing the same row operations on the identity matrix until it becomes the given matrix.

1. Start with the given matrix as the starting point.
2. Perform row operations on the given matrix to make the leading entry of the first row equal to 1.
3. Perform row operations to make all the entries below the leading entry of the first row equal to 0.
4. Move to the second row and repeat steps 2 and 3.
5. Continue this process until the matrix is in echelon form.

Each row operation can be represented by an elementary matrix, so the sequence of elementary matrices required to transform the matrix into echelon form can be obtained from the row operations performed on the identity matrix.