The set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal basis for W. Assume the vectors are in the order *1-*2- -7 8 -6 The orthogonal basis produced using the Gram-Schmidt method for W is (Type a vector or list of vectors. Use a comma to separate vectors as needed.)

Express v = (-i, 2 + i, -1) as a linear combination of the following basis vectors given below.  Justify your answer. (see image)

Find the value of K that lets the vectors form a basis

Use the Gram-Schmidt process to convert the given set of vectors to an orthogonal basis with respect to the given inner product. (Apply the Gram-Schmidt process in the order the vectors are given and do not normalize.) The set {2x + 1,x², 9} with respect to the inner product (p, q) = p(−1)q(-1) + p(0)q(0) + p(2)q(2).

in terms of linear algrebra

please dont provide hand written solution K If B is the standard basis of the space P3 of polynomials, then let B = {1, t, t², t³). Use coordinate vectors to test the linear independence of the set of polynomials below. Explain your work. (-3-t)³, (-2-t)², 31+31t+10² +³ Write the coordinate vector for the polynomial (-3-t)³, denoted p₁.

Find the scalar and vector projections of b onto a. a =    −3, −6, 2   ,    b =    2, 1, 1

Please show clear work

2- Verify that the set of vectors (-0.6, 0.8, 0), (0.8, 0.6, 0), (0, 0, 1) form an orthonormal basis for R³, then obtain an orthonormal basis from them. Express (3,7,-4) as a linear combination of the orthonormal basis. 3- Determine whether the following sets of vectors are linearly dependent or linearly independent. a) (1,1,0), (0,0,1), (0,1,1) in R³ b) (1,0,0), (2,2,0), (3,3,3) in R³

Create a basis of R¹ containing vectors (1,-1,3, 2) and (2,1,3, 4) by adding basis vectors of the orthogonal comlement to their span.