10. to solve a system of equations using the matrix method, use elementary row operations to transform the augmented matrix into one with then, proceed back to substitute. a. zeros in its final column b. an inverse c. zeros below the diagonal d. gaussian elimination

  C. zeros below the diagonal

Step-by-step explanation:

Upper echelon form (zeros below the diagonal) corresponds to a system of equations that has one equation in one variable, one equation in two variables, and additional equations in additional variables adding one variable at a time.

The single equation in a single variable is easily solved, and that result can be substituted into the equation with two variables (one of which is the one just found) to find one more variable's value. This back-substitution proceeds until all variable values have been found.

The process of producing such a matrix is called Gaussian Elimination.

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The back-substitution process effectively makes the matrix be an identity matrix (diagonal = ones; zeros elsewhere) and the added column be the solution to the system of equations.