Question: Consider the linear function L: R3 R defined by L(x, y, z) = 3x - y + 2z. Write down the vector a R3 such

Consider the linear function L: R3 †’ R defined by L(x, y, z) = 3x - y + 2z. Write down the vector a ˆˆ R3 such that L[v] = (a, v) when the inner product is
(a) The Euclidean dot product,
(b) The weighted inner product
(v, w) = v1w1 + 2 v2w2 + 3 v3 w3,
(c) The inner product defined by the positive definite matrix

012 121 2

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