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Find an equation involving $g, h,$ and $k$ that makes this augmented matrix correspond to a consistent system:$$\left[\begin{array}{rrrr}{1} & {-4} & {7} & {g} \\ {0} & {3} & {-5} & {h} \\ {-2} & {5} & {-9} & {k}\end{array}\right]$$

The system is consistent if $2 g+h+k=0$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 1

Systems of Linear Equations

Introduction to Matrices

Maruska B.

March 12, 2021

The 4 should be negative. [ 1 - 4 7 g ]

Dk B.

December 8, 2021

the second matrix should be -3 instead of 13.

the matrix has the value -4 not 4

although the answer is right, as the question was copied wrong the explanation is also wrong.

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So for this problem were asked to find the values of G, H and K that will make this system consistent. And to do that, we're going to start by trying to put the system in triangular form. So first we'll get rid of that negative, too. And we're keeping track of what's happening to the variables on the right. You So that gives us a K plus two g in that bottom, right? And so now we're going to try to get rid of that. Ah, 13. But we'll know this, actually, that we have this minus 55 And so, actually, what happens is if we have these two equations together, just as they are, we end up with zeros in the bottom, and we have actually no one here or no way Thio go about getting a triangular form here. And because of that, it means that the only way that we're going to be able to actually say that this equation is consistent is if this bit here h plus que plus two g turns out working out to zero, in which case we'll be able to create something consistent from the top to Rose and So the solution to our problem is that in order to create a consistent matrix here, we're going to need HBO's Capel's to G to be zero.

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