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If the equation $H \mathbf{x}=\mathbf{c}$ is inconsistent for some $\mathbf{c}$ in $\mathbb{R}^{n},$ what can you say about the equation $H \mathbf{x}=\mathbf{0} ?$ Why?

the equation $H x=0$ will not have the trivial solution only. It will have non - trivial solutions as well.

Algebra

Chapter 2

Matrix Algebra

Section 3

Characterizations of Invertible Matrices

Introduction to Matrices

Oregon State University

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Baylor University

University of Michigan - Ann Arbor

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problem again. We need to apply the convertible metric spirit. So we know that each eggs equal see is inconsistent. So this isn't inconsistent. Sorry. So this is inconsistent end. So this is actually the negation uh, r g? I'll just write down here negation, uh, off part G. Uh, I am t Okay. So, equivalent in these seas, we have indication of I am t And we need to figure out the equation. It each acts because zero So in our you know where your burnable matrix theory room. We have part d r d. That is message. I just write down. Ready down again. Artie is equivalent to RG. So the litigation off party is equivalent to location off our G. That means Oh, what part D says if the question, actually zero has only the trivial solution. So indication off Part D. So that means what? What? What we can see about each axe equal zero, That is the system has nontrivial solution. Nontrivial solution. So that's our conclusion.

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