[理工] [線代]-least squares相關問題
1.Find the least squares solution to each of the following systems.
(a) x1 + x2 = 3 (b) (c)
2x1 - 3x2 = 1 BALABALA BALABALA
0x1 + 0x2 = 2
^
2.For each of your solutions x in Excercise 1 ：
^
(a) Determine the projection p = Ax.
^
(b) Calculate the residual r(x).
^
(c) Verify that r(x) € N(A^T).
3.For each of the following systems Ax = b, find all least squaressolutions.
╭ ╮ ╭ ╮
│ 1 2 │ │3│
(a) A =│ 2 4 │, b =│2│ (b) BALABALA
│-1 -2 │ │1│
╰ ╯ ╰ ╯
4.For each of the systems in Exercise 3, determine the projection p of b onto
R(A) and verify that b-p is orthogonal to each of the column vectors of A.
嗯嗯……
我第一題和第三題都會算，
可是第二和第四題我不懂它是要求什麼＠＠
可以請大大講解順便示範一下嗎？
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