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Rewrite the (numerical) matrix equation below in symbolic form as a vector equation, using symbols $\mathbf{v}_{1}, \mathbf{v}_{2}, \ldots$ for the vectors and $c_{1}, c_{2}, \ldots$ for scalars. Define what each symbol represents, using the data given in the matrix equation.$$\left[\begin{array}{rrrrr}{-3} & {5} & {-4} & {9} & {7} \\ {5} & {8} & {1} & {-2} & {-4}\end{array}\right]\left[\begin{array}{r}{-3} \\ {2} \\ {4} \\ {-1} \\ {2}\end{array}\right]=\left[\begin{array}{r}{8} \\ {-1}\end{array}\right]$$

$c_{1} v_{1}+c_{2} v_{2}+c_{3} v_{3}+c_{4} v_{4}+c_{5} v_{5}=v_{6}$Where $c_{1}=-3, c_{2}=2, c_{3}=4, c_{4}=-1, c_{5}=2$ and $v_{1}=\left[\begin{array}{c}{-3} \\ {5}\end{array}\right], v_{2}=$$\left[\begin{array}{c}{5} \\ {8}\end{array}\right], v_{3}=\left[\begin{array}{c}{-4} \\ {1}\end{array}\right], v_{4}=\left[\begin{array}{c}{9} \\ {-2}\end{array}\right], v_{5}=\left[\begin{array}{c}{7} \\ {-4}\end{array}\right], v_{6}=\left[\begin{array}{c}{8} \\ {-1}\end{array}\right]$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 4

The Matrix Equation Ax D b

Introduction to Matrices

Campbell University

McMaster University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

02:04

In Exercises $5-8,$ use th…

01:10

If $\mathbf{a}_{1}=\left[\…

01:23

01:07

Write the system of equati…

01:36

In Exercises 9 and $10,$ w…

01:08

05:08

Determine the solution set…

00:40

For the following exercise…

00:55

Write each system as a mat…

09:42

Evaluate the determinant o…

All right. So for a problem, 28 we just need to apply. Apply our definition for the, uh, definitely 48 times, eight times acts. So, um, here we first need to notice that this is Ah. First were, uh the first matrix is to buy five. So that means we will have five vectors. That is all the columns. That is the So those five directors are from the columns of the giver and make 68 So just write down what you want me to be three and before and be fine. Okay. And since there are five actors, so there will also be five skaters. See? One seat too. C three, c four and C five. Okay, so here, See one. I just tried. I just tried to write down what these symbols mean. See, one or C, I will be the ice entry. Uh, vector. I'll just write it down next of 3 to 4 to 12 Negative. Three to excuse me. Make it 32 or a negative one, too. Okay. And be won, or B, I missed three. I've column of the Given matrix, which is negative. 3592497 netting three by elected 497 and the second row is 581 elected to eight one active. Too active. So that's it for it's for our solution for quiet problem 28.

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