15. The augmented matrix A represents a system of three real-valued equations in three unknowns. Which of the answer choices would result from the usual first step of applying Gauss-Jordan elimination?
A = (1 4 2 3)
A = (2 9 13 18)
A = (3 10 8 15)
To apply Gauss-Jordan elimination to the augmented matrix A, we need to perform elementary row operations to transform the matrix into its reduced row echelon form. The first step in Gauss-Jordan elimination is to create a pivot in the top left corner of the matrix.
To find the answer choice that represents the first step of Gauss-Jordan elimination, we need to determine which answer choice creates a pivot in the top left corner of the matrix.
Let's look at the first column of each answer choice:
Option 1: The first entry in the first column is 1, which is a suitable pivot candidate.
Option 2: The first entry in the first column is 2, which is also a suitable pivot candidate.
Option 3: The first entry in the first column is 3, which is a suitable pivot candidate as well.
Since all of the answer choices have a suitable pivot candidate in the top left corner, any of the options could be the result of the usual first step of applying Gauss-Jordan elimination.