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In Exercises 15 and $16,$ fill in the missing entries of the matrix, assuming that the equation holds for all values of the variables. $$\left[\begin{array}{lll}{?} & {?} & {?} \\ {?} & {?} & {?} \\ {?} & {?} & {?}\end{array}\right]\left[\begin{array}{l}{x_{1}} \\ {x_{2}} \\ {x_{3}}\end{array}\right]=\left[\begin{array}{c}{3 x_{1}-2 x_{3}} \\ {4 x_{1}} \\ {x_{1}-x_{2}+x_{3}}\end{array}\right]$$

$\left[\begin{array}{ccc}{3} & {0} & {-2} \\ {4} & {0} & {0} \\ {1} & {-1} & {1}\end{array}\right]\left[\begin{array}{l}{x_{1}} \\ {x_{2}} \\ {x_{3}}\end{array}\right]=\left[\begin{array}{c}{3 x_{1}-2 x_{3}} \\ {4 x_{1}} \\ {x_{1}-x_{2}+x_{3}}\end{array}\right]$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 9

The Matrix of a Linear Transformation

Introduction to Matrices

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Lectures

01:32

In mathematics, the absolu…

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In Exercises 15 and $16,$ …

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Use Cramer’s rule to compu…

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In Exercises $17-26,$let

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In the current problem, we have to find out the metrics for which, if we multiply them with x one x two and next three, we should get the final answer to be three x one minus to x three in four x one and then x one minus X two Glass Extreme. Now let us Before we answer this question, let us try to do the same thing with little easy numbers. Okay, so, for example, we're multiplying the same next one next to an extreme. And here are some e b. C. Right. So what will be the answered x one plus B x two plus see extreme. So if you see whatever coefficients x x, one extra, an extra is having those air only written in a row format. Over here, A, B and C are there were writing them in a row format. So let's go ahead and do the same. Afford this. What is the coefficient of X? It's excellent. It is three. What is the coefficient of X to? Well, the X two term is not there. So then it must be zero. And what is the coefficient of X three? It is minus two correct same way in the next one. For X one, it is for for extra. It is zero for ex treaties against zero and the same way. Here it is. One minus one and plus one. So one minus one. What? So this is our answered simple.

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