Question

Given u, find the coordinates for v in the subspace spanned by

[-1] [0]
[-2] and [0]. Note that u and v are orthogona
[2 ] [5]

Answer 1

To find the coordinates for v in the subspace spanned by the given vectors, we can set up a dot product equation with u and one of the basis vectors. The dot product equation will allow us to solve for the coordinates of v.

Step-by-step explanation:

The given problem involves finding the coordinates for v in the subspace spanned by the vectors [-1] [0] [-2] and [0], given that u and v are orthogonal.

To find the coordinates for v, we can set up the dot product between u and one of the basis vectors in the subspace. This will give us an equation that we can solve for the coordinates of v.

Let's take the dot product between u and the first basis vector [-1]. The dot product is calculated by multiplying the corresponding components: u1*(-1) + u2*0 + u3*(-2) = 0. This equation should be satisfied by the coordinates of v.