Question

Investigate whether or not it is possible to find numbers s and t which satisfy the possible vector equation.
Also, find s and t if it is possible, which in this case it is, but I'm getting wrong values/incorrect answers.

(b) \[\left(\begin{matrix}-1 \\ -2\\ 3 \end{matrix}\right)+s\left(\begin{matrix}1 \\ 2\\ -1 \end{matrix}\right)+t\left(\begin{matrix}3 \\ -1\\ 1 \end{matrix}\right)=\left(\begin{matrix}5 \\ 3\\ 4 \end{matrix}\right)\]

Answer 1

-1+s+3t=5
-2+2s-t=3
3-s+t=4

s+3t =6 ---(1)
2s-t=5 ---(2)
s-t=-1 ---(3)

(2)-(3):
s=6

put this into (3),
6-t=-1
t=7

put t=7 and s=6 into (1)
6+3(7)=6
27=6
which is contradiction

Therefore, it is impossible to find s and t

Answer 2

-1+s +3t = 5 ------(1)
-2+2s-t = 3 -------(2)
3-s+t = 4 --------(3)

adding (2) and (3) you get

1+s = 7
s=6
then 3-6+t=4
t=7

replacing s and t in (1)

-1+6+21 =5 !! false

so it is not possible to find s and t

Answer 3

Hmm... The answer in the text book says 3,1 ....? But i got values 6 and 7 aswell..?

Answer 4

I hope you understand my workings :'(

Answer 5

Yes, I do. Thanks Callisto... That's the right answer.

Answer 6

coco is right

Answer 7

I was shocked when they said it's not possible to find s and t...

Answer 8

Wait.. it seems they have a point...

Answer 9

you get 3and 1 if you solve using equations (1)&(2) but if you use equations (2)&(3) you will get 6 and 7
well in both cases if you replace in the remaining equation it will give you a wrong answer
so still the answer is "it is impossible to find s and t"

Answer 10

Hmm. I got 6 and 7 and 3 and 1, but the textbook says 3 and 1...? So what do I do?

Answer 11

1. write "it is impossible to find s and t"
2. ask your teacher
and vice versa

Answer 12

Hmm, don't have a teacher... just the textbook :P so, I'll just note it as impossible.