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In Exercises 13 and 14 , assume that $A$ is row equivalent to $B .$ Find bases for Nul $A$ and $\operatorname{Col} A .$$$A=\left[\begin{array}{rrrr}{-2} & {4} & {-2} & {-4} \\ {2} & {-6} & {-3} & {1} \\ {-3} & {8} & {2} & {-3}\end{array}\right], B=\left[\begin{array}{llll}{1} & {0} & {6} & {5} \\ {0} & {2} & {5} & {3} \\ {0} & {0} & {0} & {0}\end{array}\right]$$

$\left\{\left[\begin{array}{c}{-2} \\ {2} \\ {-3}\end{array}\right],\left[\begin{array}{c}{4} \\ {-6} \\ {8}\end{array}\right]\right\}$

Calculus 3

Chapter 4

Vector Spaces

Section 3

Linearly Independent Sets; Bases

Vectors

Missouri State University

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Harvey Mudd College

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thing. This problem we're going to Memphis is and now were Don't let the medics be. Is there a little echo for actually roll echo? Horrible magics. Hey, so we're us to find the basis for full of hay and for no, uh, you know, give it two columns, periods, columns are the basis or column A. And from this row equal, we can find the columns it is. First, call them it Hurt column And the hello said in the basic structure for Cole a would be 1213 negative by negative pipes, your fire and negative 3 to 5 Negative. These are the 1st 3rd and fifth columns. A medic. It's a seven part B. Where to find the basis vector for No way. So we're basically trying to find this system off for eggs equals zero. Um, using the Rocco before we can form a set of equations. And that is from 1st 1 Explain, Izzy, come through negative, too. That's too minus for its four minus fired eggs. Now, from the second polo, we know they're five. Fixed. Three is equally true. 764 minus eight expired. Then from the third row, we know that 99 expired is zero. So this tells us that explain the zero. And in Hubei, zero in the second and the person in question. Uh, you're my next Want to be negative two x two Negative two x two Minus for export, eh? Extreme to be seven or 564 minus seven over five. Exports is this term is zero. So, as you can see Thanks. Do the next four are free. Really? So we can write this system as exits. Take your food X one x to extreme export and its fire, and that is equal to X to needed to 1000 plus is four negative or 07 over 51 And here and these factories are the basis for no

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