Let B = [V1, V2, V3] and B' = [W1, W2, W3] be bases for a...

Question

Question

Let B = [V1, V2, V3] and B = [W1, W2, W3] be bases for a vector space V and Vi = W1 + 5W2 – W3 U2 = W1 U3 -W1 - 4w2 – 2w3 If

math algebra

Answer 1

Answer #1

given that , vector v relative to basis B is

(v)_B=(1,-1,2)

we can write

v=1.v_1-1.v_2+2v_3=v_1-v_2+2v_3

substituting for v_1,v_2,v_3 we get

v=(w_1+5w_2-w_3)-w_1+2(-w_1-4w_2-2w_3)

which on simplifying we get

v=-2w_1-3w_2-5w_3

so we get coordinates as

$\boldsymbol{c_1=-2 , \ c_2=-3 , \ c_3=-5}$

Answer 2

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