線性代數›Ch4 線性轉換
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◀ LA 8/16
8. Coordinate Vector、Change of Basis
#LA-04-008易Coordinate VectorChange of Basis

Let S={V1,V2,V3}S = \{V_1, V_2, V_3\} and T={U1,U2,U3}T = \{U_1, U_2, U_3\} be the ordered bases for the vector space R3\mathbb{R}^3, where V1=[−1 2 1]TV_1 = [-1\ 2\ 1]^T, V2=[0 1 0]TV_2 = [0\ 1\ 0]^T, V3=[−2 2 1]TV_3 = [-2\ 2\ 1]^T, and U1=[−1 1 0]TU_1 = [-1\ 1\ 0]^T, U2=[0 1 1]TU_2 = [0\ 1\ 1]^T, U3=[2 1 1]TU_3 = [2\ 1\ 1]^T. For a vector V in R3\mathbb{R}^3, the coordinate vector of V with respect to the basis T is [2 3 1]T[2\ 3\ 1]^T. The coordinate vector of V with respect to the basis S is [M N P]T[M\ N\ P]^T. What is mod(round(∣M+N+P∣),5)\text{mod}(\text{round}(|M+N+P|), 5)?

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