课程名称︰线性代数 课程性质︰必修 课程教师︰冯蚁刚 开课学院：电资学院 开课系所︰电机系 考试日期（年月日）︰2012/03/22 考试时限（分钟）：50分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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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