To transform the given matrix into an upper triangular matrix, we perform a series of row operations. First, we use the first row to zero out elements in the first column of the lower rows, and then use the second row to zero elements in the second column of the third row. The result will be a matrix where all elements below the main diagonal are zero.
To change the given matrix into an upper triangular matrix, we need to use elementary row operations. An upper triangular matrix is a square matrix where all the elements below the main diagonal are zero. Here's the given matrix:
[7 2 4]
[1 3 2]
[-1 1 6]
Step 1: Use the first row to zero out elements in the first column of rows 2 and 3.
Multiply the first row by 1/7 and add to the second row (multiplied by -1) to get a new second row.
Multiply the first row by 1/7 and add to the third row (multiplied by 1) to get a new third row.
Step 2: Use the new second row to zero out elements in the second column of the third row.
Multiply the second row by 1/(3 - 2/7) and add to the third row (multiplied by -1) to get a new third row.
Step 3: The third row doesn't need changes because it is already an upper triangular form.
The final upper triangular matrix after applying the steps should look like this:
[7 2 4]
[0 a b]
[0 0 c]
Where a, b, and c represent the values obtained after performing the row operations.