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In Exercises $5-8,$ use the definition of $A \mathbf{x}$ to write the matrix equation as a vector equation, or vice versa.$$\left[\begin{array}{rr}{7} & {-3} \\ {2} & {1} \\ {9} & {-6} \\ {-3} & {2}\end{array}\right]\left[\begin{array}{l}{-2} \\ {-5}\end{array}\right]=\left[\begin{array}{r}{1} \\ {-9} \\ {12} \\ {-4}\end{array}\right]$$

$\left[\begin{array}{c}{1} \\ {-9} \\ {12} \\ {-4}\end{array}\right]$

01:34

Runpeng L.

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 4

The Matrix Equation Ax D b

Introduction to Matrices

Missouri State University

Baylor University

Lectures

01:32

In mathematics, the absolu…

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In Exercises $5-8,$ use th…

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In Exercises $5-8,$ the au…

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In Exercises 9 and $10,$ w…

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For the following exercise…

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In Exercises 13 and $14,$ …

So if they want us to rewrite this equation here, um, to the vector sum, what will do is what We just take this negative too. So we multiply it by this first road here, so it's going to be negative, too. And then we have 7 to 9 minus three, and then we take this negative five and then multiply this one by the second row. So this is gonna be negative. Five. And then you have negative 31 negative 62 And in the right side of the equation, will we just keep that as the same? So one negative line 12 negative four. And then we can just double check really quickly that these do actually equal each other. So if we were to do negative too. So this this isn't really needed for this next step. So technically, we're done at this point, But just to kind of make sure that these are equal. So over here we would distribute the negative tube, so that gives us negative 14 negative for negative 18 and six. And then we're gonna add this to when we distribute the negative five. So that gives us 15 negative five negative. 30 of not negative. 30. Positive 30 and then negative. 10. And so is this equal to what we have over here? So let me just put, like, a little question mark. So let's see. Negative. 14 plus 15 is one, so that's good. Negative for plus negative. Five is negative. Nine. That's good. Negative. 18 plus 30 is 12. That's also good. Six minus 10. Negative for So yeah, it does look like that is good beer. So, again, this is just more kind of double checking. Um, that this answer is correct. And all we really needed to stop at was what we had in that red box there.

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