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[M] Determine whether $\mathbf{w}$ is in the column space of $A,$ the null space of $A,$ or both, where $$\mathbf{w}=\left[\begin{array}{l}{1} \\ {2} \\ {1} \\ {0}\end{array}\right], \quad A=\left[\begin{array}{rrrr}{-8} & {5} & {-2} & {0} \\ {-5} & {2} & {1} & {-2} \\ {10} & {-8} & {6} & {-3} \\ {3} & {-2} & {1} & {0}\end{array}\right]$$

$w \in \operatorname { Col } A$

Calculus 3

Chapter 4

Vector Spaces

Section 2

Null Spaces, Column Spaces, and Linear Transformations

Vectors

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in this problem were given a directive W and then they say, and nowhere else to turn with the new is indeed home space or and whether it is indeed no space, eh? So I used that to do that. I used our recommitment to find the role Ackman form off the augmented system A that you could use meth at this moment. Or you could use any rental to find the oracle for your vent system. And we end up getting this matrix. Uh, 108102 01 negative. 203 000 Or Warm and waas Wrong years old zeros. And as you can see from this, our lamented metrics aerobic purple X because be this system is court system. So this means that w is actually mean home. A got to take 40 check weather, W's and no pay or not. We're gonna multiply, Amy, don't you? And if you do so you end up with a vector off zero. So this proves that the blue is also in no

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