Question

Which of the following is the correct form of the matrix below after performing row operations to get it into a reduced row echelon form?

(A matrix representation would be provided for the question)
A) The original matrix
B) Row-echelon form
C) Reduced row-echelon form
D) A different matrix not provided in the options

Answer 1

The correct form of the matrix after row operations is reduced row echelon form (C).

Step-by-step explanation:

The correct form of the matrix after performing row operations to get it into reduced row echelon form is the Reduced row-echelon form (C). Reduced row echelon form is the most simplified form of a matrix, achieved by applying row operations such as scaling, swapping, and adding multiples of rows to eliminate non-zero entries below and above leading ones. It has the following properties:

1. The leading coefficient (the leftmost non-zero entry) of each non-zero row is 1.

2. The leading coefficient of each non-zero row is the only non-zero entry in its column.

3. Any row containing all zeros is at the bottom of the matrix.