a) show all 3 vectors are linearly independent. I calculated the det and it is 0 so they are all linearly independent.
It's exactly the other way around : iff the determinant of the matrix formed by the vectors is zero are these vectors lin. dependent ...and they
indeed are lin. dependent!
I also found the zero vector, v3, which is v3 = 3*v2 - 2*v1
b) describe, geometrically, the subspace of r3 spanned by v1, v2 and v3.
i do not know how to do this. please help.
It's just the plane spanned by .
c) find a vector w such that v1 and v2 and w are linearly independent.
this one i'm not sure about, my teacher said i could just calculate the cross product.
Of course: the cross product of two vectors is a vector perpendicular to both vectors and, thus, lin. independent of them...
the cross product of v1 and v2 is (-1,-1,1). now what do i do with this? how do write the answer?
Just write that are lin. ind., and check this showing their determinant is not zero!