Given vectors \mathbf{v} = ⎡⎣−4−38⎤⎦ v= ⎣ ⎢ ⎡ −4 −3 8 ⎦ ⎥ ⎤ , \mathbf{b_1} = ⎡⎣123⎤⎦ b 1 = ⎣ ⎢ ⎡ 1 2 3 ⎦ ⎥ ⎤ , \mathbf{b_2} = ⎡⎣−210⎤⎦ b 2 = ⎣ ⎢ ⎡ −2 1 0 ⎦ ⎥ ⎤ and \mathbf{b_3} = ⎡⎣−3−65⎤⎦ b 3 = ⎣ ⎢ ⎡ −3 −6 5 ⎦ ⎥ ⎤ all written in the standard basis, what is \mathbf{v}v in the basis defined by \mathbf{b_1}b 1 , \mathbf{b_2}b 2 and \mathbf{b_3}b 3 ? You are given that \mathbf{b_1}b 1 , \mathbf{b_2}b 2 and \mathbf{b_3}b 3 are all pairwise orthogonal to each other
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