[試題] 102上 蘇柏青 線性代數 期中考
課程名稱︰線性代數
課程性質︰工管系科管組必修
課程教師︰蘇柏青
開課學院:管理學院
開課系所︰工管系科館組
考試日期(年月日)︰2013.11.09
考試時限(分鐘):14:20~17:20 (結束時間不確定,很多人都提早交)
是否需發放獎勵金:是
(如未明確表示,則不予發放)
試題 :
╭ 1 2 1 0 ╮
│ │
│ 3 6 1 1 │
1. (75%) Let the 3x4 matrix A be defined by A = [a1 a2 a3 a4] =│ │
╰ 2 4 1 0 ╯
(a) (5%) Find the reduced row echelon form of A. Denote it by R.
(b) (5%) Find an invertible matrix P such that R = PA.
-1
(c) (5%) Find P . (是P的負一次方的意思)
(d) (5%) Find rank A and nullity A.
(e) (5%) Find the pivot columns of A.
(f) (25%) Do the same things for A', where A' = [a4 a3 a2 a1]. (Use notations
R' and P' for the corresponding matrices).
T
(g) (25%) Do the same things for A2 where A2 = A . (Use notations R2 and P2
for the corresponding matrices).
(簡單來說,(f)和(g)小題,就是要用不同的矩陣,把(a)~(e)再全部走一次)
2 3
2. (25%) Consider a linear transformation T: R ---> R. Suppose
╭ 3 ╮ ╭ 1 ╮
╭ 0 ╮ │ │ ╭ 1 ╮ │ │
T (│ │) = │ 2 │ and T (│ │) = │ 2 │.
╰ 1 ╯ │ │ ╰ 2 ╯ │ │
╰ 1 ╯ ╰ 3 ╯
╭ 0 ╮
(a) (5%) Find T(│ │).
╰ 2 ╯
╭ 1 ╮
(b) (5%) Find T(│ │).
╰ 0 ╯
(c) (5%) Find the standard matrix A for T (i.e. the matrix A such that
T(x) = Ax).
(d) (5%) Is T onto? Why?
(e) (5%) Is T one-to-one? Why?
拿到考卷時,全班驚呼:考卷只有一面?! 殊不知無窮迴圈正在等大家
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