Find the complete solution of the linear system, or show...

Transcript

00:01 Okay, so for this question, we're going to solve this system of linear equations or show that the system of equations is inconsistent.

00:11 So first i'm just going to label these equations, one, two, and three.

00:18 And what we can do is try to eliminate the x variable from a couple of these equations so that if the, we cannot have two equations that are only two variables rather than three, make things a little simpler.

00:32 So the first thing we'll do is an operation equation 2 minus equation 1.

00:39 So that we'll have x minus x and we'll get 0x.

00:44 We'll also do equation 3 minus 2 times equation 1.

00:49 So that we'll have 2x minus 2 times x is 0x also.

00:53 So that will eliminate the x variable from both the second and third equations.

00:59 We'll do the equation to operation first.

01:02 So x minus x is 0.

01:04 So we'll cross that out as 0.

01:09 Then we have 2y minus y, which is just y.

01:13 Then we have negative 3 z minus negative z is negative 2 z.

01:20 Then we have negative 3 minus 0 is negative 3.

01:25 And this is the new equation 2.

01:29 So the next operation we get 2x minus 2 times x is 0x.

01:35 So we'll cross that out and it's 0.

01:37 Then we have 3y minus 2 times y is just y.

01:45 Then we have negative 4 z minus 2 times negative z is negative 2 then we have negative 3 minus 0 or minus 2 times 0 is negative 3.

02:01 Now you may notice that these two equations are actually exactly the same...

Question

Find the complete solution of the linear system, or show that it is inconsistent. $$\left\{\begin{array}{rr} x+y-z= & 0 \\ x+2 y-3 z= & -3 \\ 2 x+3 y-4 z= & -3 \end{array}\right.$$

Question

Find the complete solution of the linear system, or show that it is inconsistent. $$\left\{\begin{array}{rr} x+y-z= & 0 \\ x+2 y-3 z= & -3 \\ 2 x+3 y-4 z= & -3 \end{array}\right.$$

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