Let u1 = [1, 2, 1], u2 = [0, 1, 0], u3 = [-1, 0, 1], and take B = u1, u2, u3. Find the vector v

Name: Let u1 = [1, 2, 1], u2 = [0, 1, 0], u3 = [-1, 0, 1], and take B = u1, u2, u3. Find the vector v with coordinates [v]B = [2, 4, -3]. v = [ , , ]. Find the coordinates of the vector w = [-1, 7, 7] in the basis B. [w]B = [ , , ].
Uploaded: 2023-09-16T18:19:57-08:00
Duration: 2 min 3 s
Channel: Adi S
Description: Let u1 = [1, 2, 1], u2 = [0, 1, 0], u3 = [-1, 0, 1], and take B = u1, u2, u3. Find the vector v with coordinates [v]B = [2, 4, -3]. v = [ , , ]. Find the coordinates of the vector w = [-1, 7, 7] in the basis B. [w]B = [ , , ].

Question

Narayan Hari · Accepted Answer

First, we are given that $u_1 = 1$ with coordinates $(1, 0)$ in the basis ${u_1, u_2}$. We are

Question

Let u1 = [1, 2, 1], u2 = [0, 1, 0], u3 = [-1, 0, 1], and take B = {u1, u2, u3}. Find the vector v with coordinates [v]B = [2, 4, -3]. v = [ , , ]. Find the coordinates of the vector w = [-1, 7, 7] in the basis B. [w]B = [ , , ].

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