Question

[1 0 0 1] [0 1 0 2] [0 0 1 3] A matrix is given. Determine whether the matrix is in row-echelon form.

Answer 1

A row-echelon form matrix has specific conditions that need to be met, and the given matrix satisfies all the conditions.

Step-by-step explanation:

A matrix is said to be in row-echelon form if it satisfies the following conditions:

1. All rows that consist only of zeros are at the bottom.
2. The first nonzero entry from the left (also known as the pivot) in each row is always to the right of the pivot in the row above it.
3. All entries below the pivot are zeros.

Using this definition, let's analyze the given matrix:

[1 0 0 1] [0 1 0 2] [0 0 1 3]

The given matrix satisfies all the conditions mentioned, therefore it is in row-echelon form.