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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