Find values of a, b, and c which satisfies the following equation:

Question

a(2,1,0) + b(-3,4,5) + c(2,0,3)= (-4,10,7)

Answer 1

You will have to solve 3 equations in 3 unknowns

2a - 3b + 2c = -4
a + 4b = 10
5b + 3c = 7

Answer 2

I got that far i just wasn't sure how to solve for 3 different unknowns unless I represent some unknown as the same as another unknown in the question?

Answer 3

double the 2nd and subtract from the first
-11b + 2c = -24 (#4)

#4x 3 : ---> -33b + 6c = -72
#3x 2 : ---> 10b + 6c = 14

subtract them
-43b = -86
b = 2

in #4 : -22 + 2c = -24 ,
c = -1

in #2 : a + 8 = 10
a = 2

a=2, b=2, c=-1

check:

2(2,1,0) + 2(-3,4,5) - 1(2,0,3)
= (-4,10,7)
= RS

Answer 4

great thanks :)