Re: [理工] 100交大光電工數
※ 引述《shareing ( )》之銘言：
: 最後一題
: Let V = {v1 v2 v3} be the basis of R^3 where
: [1] [-1] [0]
: v1 = [0] v2 = [ 2] v3 = [1]
: [1] [ 2] [2]
: and W = {w1 w2} be the basis of R^2 with
: [3] [5]
: w1 = [1] w2 = [2]
: Let T：R^2 -> R^3 be a linear transformation such that
: [3] [1] [5] [1]
: T [1] = [0] and T[2] = [0]
: [0] [1]
: [1]
: (c)小題 Find T[0] ok
: But
: (d)小題 Find the matrix of T relative to the standard of R^2 -> R^3.
: (e)小題 Find the matrix of T relative to W and V.
: 不會做
: 請大家給我提示
: 謝謝
(e)做這種基底變換+線性轉換建議畫路線圖
s
1. 先做[I]
w
s [3 1]
而[I] =[5 2] (W → S)
w
2. 做[T]s
不用做，就是(d)小題答案 (T:R^2 -> R^3)
v
3.做[I]
s
-1
v [1 -1 0]
而[I] =[0 2 1] (S → V)
s [1 2 2]
v v s
所以[T] =[I] [T]s [I]
w s w
希望有幫到你了
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