[考古] 線性代數/林秀峰/97上期中考
※ [本文轉錄自 FCU_Talk 看板]
作者: Rockspirit (小白～*) 看板: FCU_Talk
標題: [考題][資訊系][線性代數][林秀峰 97上期中考]
時間: Mon Nov 3 16:33:26 2008
[ 1 -2 2]
一、Let A = [-1 1 3] be 3×3 matrix Find A^-1 = ?
[ 1 -1 4]
二、Find the set of all solutions of the system of linear equations
X1 - 2X3 + X4 = 5
3X1 + X2 - 5X3 = 8
X1 + 2X2 - 5X4 = -9
三、Find λ = ? such that the following system of linear equations has
nontrival solutions and find corresponding solutions [x] to λ
[y]
(λ-1)x + 4y = 0
2x + (3-λ)y = 0
四、(1)Determine whether the points (1，2，1)、(3，4，1) and (5，6，1) are
collinear?
(2)Find an equation of the plane passing through the points (0，1，0)
(-1，3，2) and (-2，0，1)
五、Let A = [ 1 0 -2 1 0 ] be a 4×5 matrix
[ 0 -1 -3 1 3 ]
[-2 -1 1 -1 3 ]
[ 0 3 9 0 -12]
(1)Find the rank and nullity of A
(2)Find a basis for the colum space of A
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