Question

Let B1 = { u1, u2, u3 }, where u1 = (2,?1, 1), u2 = (1,?2,...

Let B1 = { u1, u2, u3 }, where u1 = (2,?1, 1), u2 = (1,?2, 1), and u3 = (1,?1, 0). B1 is a basis for R^3 .

A. Find the transition matrix Q ^?1 from the standard basis of R ^3 to B1 .

B. Write U as a linear combination of the basis B1 .

Homework Answers

Answer #1

Given, B1 = {u1,u2,u3} where u1 = (2,1,1), u2 = (1,2,1), u3 = (1,1,0).

a) The standard basis is = {(1,0,0),(0,1,0),(0,0,1)}.

Now, (1,0,0) = (1/2)*(2,1,1)+(-1/2)*(1,2,1)+(1/2)*(1,1,0)

(0,1,0) = (-1/2)*(2,1,1)+(1/2)*(1,2,1)+(1/2)*(1,1,0)

(0,0,1) = (1/2)*(2,1,1)+(1/2)*(1,2,1)+(-3/2)*(1,1,0)

Therefore, the transition matrix from the standard basis of R3 to B1 is : Q = .

b) Here is no information about U. So, it can't be written as linear combination of the basis B1.

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