Apply the Gram-Schmidt orthonormalization process to transform the given basis for R" into an orthonormal basis. Use the vectors in the order in which they are given. B = {(15, 8), (1, 0)} u2 =

Use Gram-Schmidt process to transform the basis{(1, 1, 1), (0, 1, 1), (1, 2, 3)}into an orthonormal basis.

Use the inner product (u, v) = 2uzV1 + uzv2 in R2 and the Gram-Schmidt orthonormalization process to transform {(-2, 1), (2, 9)} into an orthonormal basis. (Use the vectors in the order in which they are given.) u1 = uz =

Apply the Gram-Schmidt process to obtain an orthonormal basis for the 51 space spanned by the vectors 4 6 Show your work.

You are given the following vectors in terms of their components in the i, j, k basis: A = 11+1j+2k B = 11+-1j+2k C=0i+1j+-1k Use this set of vectors to construct a set of orthonormal basis vectors. To enter unit vectors, select "Vectors" on the PhysPad that opens when you click on the answer box. Select the "hat" and enter i, j, or k in the provided space using the buttons on the PhysPad. Once entered, you have to hit the right-arrow key or tab to move the cursor out from under the hat. If you do it incorrectly you will see the hat out of position over the vector. Please review your answer before submission. Take the first vector to be in the direction of A. V₁ = Take the second vector to be in the A-B plane. V₂ = 1 + 2/ V3 = i + 0} − k - √5 31 The third vector should be perpendicular to the A-B plane in a right-handed sense.

find an orthonormal basis of the space spanned by the vectors u1= <3, -4, 5> and u2= <-3, 14, -7>

Use the inner product (u, v) = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to transform {(2, 1), (-2, -7)} into an orthonormal basis. (Use the vectors in the order in which they are given.) u1 = u2 =

Apply the Gram-Schmidt algorithm to construct an orthonormal basis out of the vectors V₁ = (1,5), V₂ = (-3, 3).

00 Find the coordinate matrix of x relative to the orthonormal basis B in R". {(름, 승, 이), (-승) 릉, 이) (0, 0, 1} 3 4 4 3 x = (10, 20, 5), B = 5' 5 5' [x]B =

V = Span ({··]}) Find an orthonormal basis of R³ that contains the vector 圓