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If $\mathbf{b} \neq \mathbf{0},$ can the solution set of $A \mathbf{x}=\mathbf{b}$ be a plane throughthe origin? Explain.

No

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 5

Solution Sets of Linear Systems

Introduction to Matrices

Missouri State University

McMaster University

Lectures

01:32

In mathematics, the absolu…

01:11

00:24

Is it possible for an equa…

02:51

If $a, b,$ and $c$ are not…

05:05

If $ a, b $, and $ c $ are…

02:35

Show that if $a, b,$ and $…

02:20

The graph of $(x / a)+(y /…

00:28

Is 0 a solution of the equ…

01:10

If $(a, b)$ is an ordered …

02:15

Determine whether the give…

01:45

All right, so in this problem, we're even. Yeah, it's not equal to zero. And we are trying to figure out whether the solution off a X equals B can be the plane through the origin. So in this case, um, I'll first tell you that the answer is no. Why? Why is it white is no. So let's suppose suppose the solution said passes through as it passes through a region which is started zero vector and then we will prove by contradiction. So since the solution said passes through the origin, then zero has to be a solution. Oh, axe. Because he all right now, now, since zero it's a solution. Then we put zero but the value here, the bedroom into the system. So that is eight times zero because be and eight times theories is it is exactly zero. So we get e zero. So he's a zero factor here. I recall that we were assuming that it is not equal to zero from our from the beginning. So this is a contradiction. So we're done. That means it's impossible to have this a plane to have the plane that passing through the origin. If we have the condition here, that B is not equal to zero

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