Matrix Question: How to find sol'n to 4x - 7y + 5z = 13? (Mine ans. is wrong)

[pmaz8]

Solve the equation: \(\displaystyle 4x\, -\, 7y\, +\, 5z\, =\, 13\)

. . .\(\displaystyle \left[\begin{matrix}x\\y\\z\end{matrix}\right]\, =\, \left[\begin{matrix}13/4\\-13/7\\13/5\end{matrix}\right]\, +\, \left[\begin{matrix}7/4\\5/7\\7/5\end{matrix}\right]\,s\, +\, \left[\begin{matrix}-5/4\\4/7\\-4/5\end{matrix}\right]\, t\)

So I'm unsure how to find the solution to this as you can see I solved for each x, y and z by putting each in terms of variables s and t but obviously this wasn't the case. I'm just unsure how this question would be answered

 

[pmaz8]

Matrix Question!

So I'm unsure how to find the solution to this as you can see I solved for each x, y and z by putting each in terms of variables s and t but obviously this wasn't the case. I'm just unsure how this question would be answered
You can view the question <link removed>

 

[tkhunny]

Please demonstrate what it is that didn't work.

 

[stapel]

Solve the equation: \(\displaystyle 4x\, -\, 7y\, +\, 5z\, =\, 13\)

. . .\(\displaystyle \left[\begin{matrix}x\\y\\z\end{matrix}\right]\, =\, \left[\begin{matrix}13/4\\-13/7\\13/5\end{matrix}\right]\, +\, \left[\begin{matrix}7/4\\5/7\\7/5\end{matrix}\right]\,s\, +\, \left[\begin{matrix}-5/4\\4/7\\-4/5\end{matrix}\right]\, t\)

How did you get a matrix from just the one equation? By what steps did you arrive at this answer?

I solved for each x, y and z by putting each in terms of variables s and t...

How did that lead to the posted result?

...but obviously this wasn't the case.

What "wasn't the case"? How "obviously"? Do you mean that "this didn't get me to the correct result"? If so, how do you know? What is the correct result?

Please be complete. Thank you!

 

[Ishuda]

Solve the equation: \(\displaystyle 4x\, -\, 7y\, +\, 5z\, =\, 13\)

. . .\(\displaystyle \left[\begin{matrix}x\\y\\z\end{matrix}\right]\, =\, \left[\begin{matrix}13/4\\-13/7\\13/5\end{matrix}\right]\, +\, \left[\begin{matrix}7/4\\5/7\\7/5\end{matrix}\right]\,s\, +\, \left[\begin{matrix}-5/4\\4/7\\-4/5\end{matrix}\right]\, t\)

So I'm unsure how to find the solution to this as you can see I solved for each x, y and z by putting each in terms of variables s and t but obviously this wasn't the case. I'm just unsure how this question would be answered

I'm unsure myself. I would expect the question to be more like "Solve the equation for x: \(\displaystyle 4x\, -\, 7y\, +\, 5z\, =\, 13\)"
in which case the answer is straight forward. Once one writes an equation with more than one variable, what one solves for should be explicitly stated, otherwise there is no unique answer.