Question

Find the echelon form of the g [[1,4,-2,3],[-3,-11,9,-5],[2,2,5,-1]]

Answer 1

To find the echelon form of the given matrix, use row operations to eliminate the entries below each pivot element.

Step-by-step explanation:

The echelon form of a matrix is a specific row-echelon form where each pivot element (the first nonzero entry in each row) is located in a column strictly to the right of the pivot elements in the previous rows. To find the echelon form of the given matrix, you can use row operations to eliminate the entries below each pivot element. Here are the steps:

1. Start with the original matrix: g = [[1, 4, -2, 3], [-3, -11, 9, -5], [2, 2, 5, -1]].
2. Choose the first nonzero entry in the first column (1) as the pivot element. Divide the first row by the pivot element to make the pivot element 1.
3. Eliminate the entries below the pivot element in the first column by adding a multiple of the first row to the second row and third row.
4. Move to the next column without a pivot element and repeat the previous steps until you reach the last column.
5. The resulting echelon form of the given matrix is: [[1, 4, -2, 3], [0, 1, -1, 1], [0, 0, 0, 1]].