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 (U)b = (1,-1,2), then the coordinates of v relative to the basis B' are c1 = C2 = and cz

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

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