question 5 Give two other vectors in R4 generated by the vec

question 5

Give two other vectors in R^4 generated by the vectors (3, 0, 1, -2), (0, 2, -3, 1), and (4, 3, -1, 0).

Solution

For two other vectors we just take some linear combinations of the given vectors.

Vector 1:

1 (3,0,1,-2) + (-1) (0,2,-3,1) + 0 (4,3,-1,0)

= (3,0,1,-2) +(0,-2,3,-1) +(0,0,0,0)

= (3,-2,4,-3)

Vector 2:

-1 (3,0,1,-2) + (-1) (0,2,-3,1) + 0 (4,3,-1,0)

= (-3,0,-1,2) +(0,-2,3,-1) +(0,0,0,0)

= (-3, -2, 2, 1)