推 s864372002 :馮ㄧˇ剛0.0。 06/22 22:02
課程名稱︰線性代數
課程性質︰必修
課程教師︰馮蟻剛
開課學院：電資學院
開課系所︰電機系
考試日期（年月日）︰2012/03/22
考試時限（分鐘）：50分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Judge if the following statements are true or false.Give a concise proof
to each true statement,anda counterexample to each false statement.
(a)A set of vector in R^n is linearly dependent if and only if one of the
vector is a multiple of one of the others. 20%
(b)If the product AB of two matrices A and B are defined and ABis a zero
matrix. 20%
2.Suppose A is an n by n nonzero matrix with the reduced row echelon form R.
Show that if rank A = m then there is a unique invertible matrix Psuch that
A = PR. 25%
Create a numerical example of an m by n nonzero matrix A with rankA < m and
reduced row echelon form R,and find two different invertible matrices P1 and
P2 such that A = P1 R = P2 R. 14%
3.Suppose A is an m by n nonzero matrix with the reduced row echelon form R.
What are the reduced row echelon forms of (a) [A O] (b)[Im A] (c)[A cA],
where c is a scalar? 21%
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◆ From: 140.112.241.100
※ 編輯: fatandy567 來自: 140.112.241.100 (06/22 14:46)
※ 編輯: fatandy567 來自: 140.112.241.100 (06/22 14:47)