LINEAR ALGEBRA Write each vector as a linear combination of

LINEAR ALGEBRA

Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, -1, 3), (5, 0, 4)} z = (1, -3, 5) z = (_______)s_1 + (_______)s_2 v = (8, -1/4, 27/4) v = (________)s_1 + (______)s_2 w = (3, -9, 15) w = (_________)s_1 + (_________)s_2 u = (7, 1, -1) u = (_________)s_1 + (_________)s_2

Solution

2x+5y = 1 ,-x = -3, 3x+4y =5

Solving gives x = 3 , y = -1

2) 2x+5y = 8 ,-x = -1/4, 3x+4y =27/4

x = 1/4, y =3/2

c)2x+5y = 3,-x = -9 3x+4y =15

x= 9, y= -3

d)2x+5y = 7, -x = 1,3x+4y =-1

No solution possible. Can not be a linear combination