Question

After applying a series of row operations to a matrix corresponding to a system of equations in x, y, and z, you arrive at the row echelon form matrix.

Answer 1

Row echelon form is a form of a matrix that represents a system of equations in a simplified manner, with zeros below the pivots. It can be obtained by performing a series of row operations on the original matrix.

Step-by-step explanation:

In row echelon form, a matrix has the following properties:

• The first nonzero entry in any row (called a pivot) is always to the right of the pivot in the row above.
• All entries below a pivot are zeros.

In terms of a system of equations, the row echelon form matrix represents the equations in a simplified form, where each row corresponds to an equation and the pivots represent the coefficients of the variables.

By performing a series of row operations on the original matrix, such as row swaps, scalar multiplication, and row additions, we can transform the matrix into row echelon form.