Solve the equation 2x + 5y - 3z = -1. Write the general solution as a matrix equation.

Question

[x] [ ] [1]
[y]= [ ] X [s]
[z] [ ] [t]

I'm supposed to fill in that blank in the middle, but I don't understand how to solve this if I'm only given one equation. please explain

Answer 1

[x] [...] [1]
[y]= [...] X [s]
[z] [...] [t]

to align it better I put dots in the blanks...and I think s and t are free variables that be be any real number

Answer 2

okay i put it wrong I'm sorry the question said

Convert to the Alternate form (Exponential INTO logarithm)

Answer 3

(2 5 -3) (x y z)^T = -1

The transpose is for readability, since it has to be a column vector.

Answer 4

I still don't really understand how to do it...

I did some guessing and ended up getting this much:

[x] [-1/2 _ _] [1]
[y]= [0 1 0] X [s]
[z] [0 0 1] [t]

however I still can't figure out the last two values in the first row.