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Let $A=\left[\begin{array}{rrr}{2} & {0} & {6} \\ {-1} & {8} & {5} \\ {1} & {-2} & {1}\end{array}\right],$ let $\mathbf{b}=\left[\begin{array}{r}{10} \\ {3} \\ {3}\end{array}\right],$ and let $W$ be the set of all linear combinations of the columns of $A .$a. Is $\mathbf{b}$ in $W ?$b. Show that the third column of $A$ is in $W .$

a. $b \in W$b. $A _ { 1 } = 0 A _ { 1 } + 0 . A _ { 2 } + 1 A _ { 3 } \Rightarrow A _ { 3 }$ is in $W$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 3

Vector Equations

Introduction to Matrices

Baylor University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

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08:08

Linear combination Let $\m…

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Linear combination $\quad$…

08:12

Let $A=\left[\begin{array}…

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02:50

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Determine $A$ c by computi…

08:16

Show that $\mathbf{x}_{1}(…

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For each pair of matrices …

10:34

Show that if the columns o…

Okay, so for problem 26 were given a three by three matrix to Davis six and negative. One, 85 and one next to two and one Dr B. Here we're given 10 33 So the first question we need to answer is, um is to find whether b is in set w where w is the set of all the new combinations of columns. Okay, so that is actually considered system the X equal speedy. And we need to We need to show whether the augmented to be tricks, eh, d, whether the system is consistent. So we consider this album ended matrix, and we do the cultural admonition to find out real radio station form, which is one There were three and five and 0111 and also for her last row. So here, if we you will take acts to be the unknown Vector X one x to next three, then bite us. Why does second roll? We know x two times x two plus x three will be one. So it's two plus x three This one and x one plus x three will be five. This despite the first rule. Sorry plus three of extreme reinfect three is five, and so it's very clear right now. We have to you questions, and we have three unknowns, so they are definitely even in many solutions to the system. So that means X equals B is consistent. So we finished our first question, and the second question we need to answer is show that 1/3 column off a C. W so he spread is just a find Alina combination off this three column vectors such that it will just a sequel to the Third Column so we can just take zero times the first column to negative 11 That's zero times the second column, 08 connected to connected to Last One Times of 615 which is the Third column. So the sum of three vectors will be just a 651 So that is just 1/3 column. But it's it is still company like Alina combination off three vectors. We just take it different skaters here, so that's it

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