Find scalars a , b , and c so that a (2, 3, -1) + b(1,0,4) +c (-3,1,2) = (7,2,5)
The answer is a =1 b = 2 and c= -1 , but I'm having trouble getting answer. I've been trying to use linear system of equations, but I'm getting some ugly numbers. Help please?
The answer is a =1 b = 2 and c= -1 , but I'm having trouble getting answer. I've been trying to use linear system of equations, but I'm getting some ugly numbers. Help please?
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2a + b - 3 c = 7
3a + 0 + c = 2
- a + 4b +2c = 5...multiply row 1 by - 4 and add to 3rd : - 9 a + 14 c = - 23..2nd --> c = 2 - 3a
- 9 a + 14 [ 2 - 3a] = 28 - 51 a = - 23---> a = 1 , c = 2 - 3 = -1 , 2 + b + 3 = 7--> b = 2
what did you do wrong ?
3a + 0 + c = 2
- a + 4b +2c = 5...multiply row 1 by - 4 and add to 3rd : - 9 a + 14 c = - 23..2nd --> c = 2 - 3a
- 9 a + 14 [ 2 - 3a] = 28 - 51 a = - 23---> a = 1 , c = 2 - 3 = -1 , 2 + b + 3 = 7--> b = 2
what did you do wrong ?