Solve Vector Equation of Matrix Using Gauss-Jordan Elimination

[thomasrules]

I have to use the Gauss-Jordan elimination to find the vector equation of the following in the format r=(a,b,c)+t(x,y,z)

Matrix: row1=[6 8 -3|9]
row2=[10-2-5|15]

I got a wrong answer so can you help me solve for the vector equation please I have this answer r=(0,0,1/2)+t(1, 0,3/2)

or x=t
y=0
z=1/2t+3/2

 

[TD]

So the given matrix is

$$\left( {\begin{array}{*{20}c} 6 & 8 & { - 3} &\vline & 9 \\ {10} & { - 2} & { - 5} &\vline & {15} \\ \end{array}} \right)$$

Could you tell us what you found after row reduction?
Also, I think you better post questions like this in "Homework & Coursework Questions".

 

[thomasrules]

So the given matrix is

$$\left( {\begin{array}{*{20}c} 6 & 8 & { - 3} &\vline & 9 \\ {10} & { - 2} & { - 5} &\vline & {15} \\ \end{array}} \right)$$

Could you tell us what you found after row reduction?
Also, I think you better post questions like this in "Homework & Coursework Questions".

Well yeah i got row1 [0 -46 0|0]
row2 [230 0 -115|345]

 

[TD]

Well yeah i got row1 [0 -46 0|0]
row2 [230 0 -115|345]

Looks good, you can still simplify though.
E.g.: [4 0 -2 0] is equivalent to [2 0 -1 0] (I divided by 2).

 

[thomasrules]

lol then why the wrong answer...It is:

3 planes intersect at (-253/30,106/15,154/15)

 

[TD]

lol then why the wrong answer...It is:

3 planes intersect at (-253/30,106/15,154/15)

Where is this coming from?
You initially said that the answer had to be "r=(0,0,1/2)+t(1, 0,3/2)" which seems more logic to me... You were almost there!