作者pattrick (派特瑞克)
看板NTU-Exam
标题[试题] 95下 黄维信 线性代数 期末考
时间Sat Jun 21 11:56:39 2008
课程名称︰线性代数
课程性质︰选修
课程教师︰黄维信
开课学院:工学院
开课系所︰工程科学与海洋工程学系
考试日期(年月日)︰2007/6/22
考试时限(分钟):
是否需发放奖励金:是
(如未明确表示,则不予发放)
试题 :
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1.Apply the Gram-Schmidt process to a=[0 0 1] , b=[0 1 1],
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c=[1 1 1] and write the result in the form A=QR.(15%)
2.True or False, with reason if true and counterexample if false:(15%)
(a) If A and B are identical except that b = 2a ,then detB=2detA
11 11
(b) The determinant is the product of the pivots.
(c) If A is invertible and B is singular, then A+B is invertible.
(d) If A is invertible and B is singular, then AB is singular.
(e) The determinant of AB-BA is zero.
3. If P is an even permutation matrix and P is odd, deduce from P +P =
1 2 1 2
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P (P +P )P that det (P +P ) = 0. (10%)
1 1 2 2 1 2
4.Find the general solution to du/dt = Au if
┌0 -1 0┐
A=│1 0 -1│
└0 1 0┘
Can you find a time at which the solution u(T) is guaranteed to return to
the initial value u(0)? (20%)
5.True of false (with counterexample if false)(15%)
(a) If B is formed from A by exchanging two rows, then B is similat to A.
(b) If a triangular matrix is similar to a diagonol matrix, it is already
diagonol.
(c) If A and B are disgonolizable, so is AB.
6.Decide between a minimum, maximum, or saddle point fot the following
functions(20%)
(a) F=-1+4[e^(x)-x]-5xsiny+6y^2 at the point x=y=0.
(b) F=[x^(2)-2x]cosy,with stationary point at x=1,y=π.
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7.Compute A A and AA , and thier eigrnvalues and unit eigenvectors, for
┌1 1 0┐
A=│ │
└0 1 1┘
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Multiply the three matrices UΣV to recover A.(20%)
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