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Suppose the coefficient matrix of a system of linear equationshas a pivot position in every row. Explain why the system isconsistent.

The system is consistent for any $m \times n$ matrix.

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 2

Row Reduction and Echelon Forms

Introduction to Matrices

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McMaster University

University of Michigan - Ann Arbor

Lectures

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In mathematics, the absolu…

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Suppose an $m \times n$ ma…

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If a Matrix has a, um, pivot position in every row, that means it must also a pivot position in every column. There's no way of explaining this. There's no other way around it because and there's a pivot position in every row and the pit to pivots cannot be in the same column. That means that we would have to have one in every row and one and, um, not necessarily every column. But let's say we had an example like this, and then it should be 00 And then we could have something like this. Perhaps so, if that is what we end up happening having we know that this system will be consistent because by definition were allowed to get it into this form. This reduced form and ultimately we know that it has enough pivot positions and enough pivot columns to make sure that the system is consistent

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