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Suppose $c \mathbf{u}=\mathbf{0}$ for some nonzero scalar $c .$ Show that $\mathbf{u}=\mathbf{0} .$ Mention the axioms or properties you use.

$\mathbf{u}=\mathbf{0}$

Calculus 3

Chapter 4

Vector Spaces

Section 1

Vector Spaces and Subspaces

Vectors

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Lectures

02:56

In mathematics, a vector (…

06:36

01:01

Show how the axioms for a …

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For the arbitrary vectors …

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02:46

Let $A$ be an $m \times n$…

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Given $u=\langle a, b\rang…

02:01

in this video, we're gonna, uh we're asked us we're gonna be solving problem number 30 of section 411 And the question basically asked us to prove that, um suppose c u equals zero for some non secular, non scaler are non zero scaler. See, And we have to show that you equals zero. And we have to mention any properties and axioms that we've used to solve this. So the first thing you wanna do is, um so here you is a vector. So you we want to add see times zero to both sides of the zero vector because, um, zero plus c times zero and this doesn't really using the axiom were just adding something that both sides to change the to keep it close in the same. So so next. We wantto factor out the sea here, see times you plus zero equals, uh, the right side's zero plus c zero, and this is possible by axiom. Uh, Axiom seven, which is basically the distributive property of vectors. Uh, which states that c times you any vector you plus me equals C u plus cv. So here we see that See you, um, equals zero it holds and then see time. Zero. There's a term for a seat, I'm sure. Alexis next to the one. Ah, basically simplify this. So we just distributed out against he See you plus C. Times zero is just zero. So, yeah, see you. Sometimes you equals See Time's zero by axiom four. And all that's left to do is divide dividing both sides by cease seethe sees cancel so new equals zero and this practice will saw.

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