What is the main purpose of reducing a coefficient matrix to row-echelon form when solving simultaneous equations?
Correct answer: B. To reveal pivots and simplify back-substitution
- A. To make every entry equal to one
- B. To reveal pivots and simplify back-substitution
- C. To change a rectangular matrix into a square matrix
- D. To calculate the transpose without multiplication
Explanation
Row-echelon form places the matrix in a triangular pattern that clearly shows pivot positions and free variables. This structure makes substitution and the analysis of solutions easier.
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