Thank you Does the vector 2 10 7 0 belong to the span of the

Thank you

Does the vector (2, 10, 7, 0) belong to the span of the three vectors u_1, u_2, u_3 defined by u_1 = (3, 10, 7, 0), u_2 = (1, 3, -2, 0), u_3 = (2, 8, 1, 0)? Justify your answer.

Solution

vectorw w is in the span : w = c1u1 + c2u2 + c3u3

( 2, 10 , 7, 0) = c1( 3, 10, 7 , 0) + c2 ( 1, 3, -2, 0) + c3( 2, 8 , 0 )

2 = 3c1 + c2 + 2c3

10 = 10c1 + 3c2 +8c3

7 = 7c1 - 2c2

0 =0 + 0 +0   No equation

Now solve the augmented matrix formed by the system of equation to see if the corresponding linear system is consistent