Answer to Question #105232 in Linear Algebra for michael

Question

Determine which vectors in R^4 belong to both span{(1, −2, −2, 3), (−1, 3, 1, −2)} and span{(0, 1, 0, −1), (1, −3, 0, 0)}.

Answer 1

Finding ,the determinant of (1,-2,-2,3),(-1,3,1,-2),(0,1,0,-1),(1,-3,0,0).

We get it -3.

Hence these four vector are linearly independent.

Hence 0 is the only vector belongs to both span{(1,-2,-2,3),(-1,3,1,-2)}

and span{(0,1,0,-1),(1,-3,0,0)}