Let 0 9 3 -3 4 = Z 0 2 1 8 -14 Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R4 spanned by x, y, and z. -1 0 -9 -3 -4 3 { -1 2 8 0 1 -14

Find the orthogonal projection of the subspace W spanned by 1 -5 -2 0 -2 -5 projw() = " -4 5 -2 -22 -37 onto

Find the orthogonal projection of v= [15 8 0] onto the subspace V of R^3 spanned by [-1 -2 -2] and [2 0 6]

Apply Gram - Schmidt process to construct an orthonormal for R4 with the standard inner product from the basis (V1, V2, V3) where V, = (1, 1, 1, 1), V2 = (1, 2, 0, 1), V3 = (2, 2, 4, 0).

2 Find an orthonormal basis of the subspace spanned by the vectors 1 -2 1 3 LoJ

Find a basis of the subspace of R* consisting of all vectors of the form X1 -8x1 + x2 -6х — 2х2 -бх — 4x2 swer should be a list of row vectors separated by commas. (Click vector to learn about entering { }.

Find a basis for the subspace of R4 spanned by S. S = {(64, -21, 9, 27), (-21, 7, -3, -9), (6, -2, 1, 3), (-12, 4, -2,-5)} 0000 0000 0000

Determine whether the set of vectors is a basis for the subspace of R^n that the vectors span.     a. {[-1, 3, 1], [2, 1, 4]} in R^3    b. {[2, 1, -3], [4, 0, 2], (2, -1, 3]} in R^3?

Use th e Gram-Schmidt Process to find an orthogonal basis for th e column spaces of the matrices

Let 2 3 [-₁] Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of R³ spanned by & and y. x = and y " JL = 2