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Let $A=\left[\begin{array}{cc}{-6} & {12} \\ {-3} & {6}\end{array}\right]$ and $\mathbf{w}=\left[\begin{array}{l}{2} \\ {1}\end{array}\right] .$ Determine if $\mathbf{w}$ is in Col $A .$ Is $\mathbf{w}$ in Nul $A$ ?

$\mathbf { w } \in \mathrm { Nul } A$

Calculus 3

Chapter 4

Vector Spaces

Section 2

Null Spaces, Column Spaces, and Linear Transformations

Vectors

Harvey Mudd College

University of Nottingham

Idaho State University

Boston College

Lectures

02:56

In mathematics, a vector (…

06:36

01:34

Let $A=\left[\begin{array}…

02:15

Determine if $\mathbf{w}=\…

00:59

With $\mathbf{u}=(-2,3,1)$…

02:37

If $A=\left[\begin{array}{…

00:33

01:25

01:50

Evaluate.$$6 a \di…

02:50

Let $\mathbf{v}_{1}=\left[…

01:05

07:12

in this problem. We're giving the metrics. I don't need words. Tiu term whether seventies and pulled a war isn't know. So let's look at the augmented system for by A and w So that is a negative six. Make every 12 6 to 1. So, um, reduced role echo for this system. Looks like one name to negative. Won't carry 000 That is You can see here from your Oh, uh, already show Echo all of these metrics. This system, it's consistent. So it means that dummy is o. K now to pass for No way we're gonna multiply a devil. So negative six negative 3 12 6 Bye bye to one. We get native six times two is 12 bust wealthy zero negative. Three times to his negative. Six plus six. We have zero. So we got the zero vector. So it means that is no

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