a. Is there a solution to the equation Ax = b where A and b are such that 21 5x= -3 b. We know that 2 -1 [2] H 2 and 5 form a basis for Col(A). Find an orthogonal basis for Col(A). c. Find the orthogonal projection of b onto Col(A). d. Explain why the equation Ax = 6 must be consistent and then find its solution.

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please solve it on paper

The set B= {1-ť, - 2t-t, 1+t-t} is a basis for P,. Find the coordinate vector of p(t) = 5- 11t- 11 relative to B. [Plg =O (Simplify your answer.)

1. Use coordinate vectors to show that (4-t)', (3-t), 2-t,and 1+ 5t – 612 +t° form a basis for P. Then find the coordinate vector for 1- 2t + 3t² – 4t³ relative to B. Find q in P 1 given that [q],

Find the representation of (-5, 5, 1) in each of the following ordered bases. Your answers should be vectors of the general form . a. Represent the vector (-5, 5, 1) in terms of the ordered basis B = {ï,j,k}. [(-5, 5, 1)]B= b. Represent the vector (-5,5, 1) in terms of the ordered basis C = (ē3, ē1, ë2). [(-5, 5, 1)]c = c. Represent the vector (-5, 5, 1) in terms of the ordered basis D = {-2, -ē1, ē3}. [(-5, 5, 1)]D=