Re: [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: BoYiShiu (哩甘有良心...?) 看板: FCU_Talk
標題: Re: [考題][資訊系][線性代數][林秀峰 97上期中考]
時間: Mon Nov 3 20:12:20 2008
※ 引述《Rockspirit (小白～*)》之銘言：
: [ 1 -2 2]
: 一、Let A = [-1 1 3] be 3×3 matrix Find A^-1 = ?
: [ 1 -1 4]
[-1 -6/7 8/7]
[-1 -2/7 5/7]
[0 1/7 1/7]
: 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
[x1] [ 2] [-1] [ 5]
[x2]= a[-1]+b[ 3]+[-7] a,b屬於R
[x3] [ 1] [ 0] [ 0]
[x4] [ 0] [ 1] [ 0]
: 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
題目有沒有抄錯...數字很醜...=.=
λ:-λ^2+4λ-11=0的解(自己用2a分之-b加減根號b平方-4ac代)
[x]=[a ]
[y] [-4a/(λ-1)] a屬於R
: 四、(1)Determine whether the points (1，2，1)、(3，4，1) and (5，6，1) are
: collinear?
Y
: (2)Find an equation of the plane passing through the points (0，1，0)
: (-1，3，2) and (-2，0，1)
-4x+3y-5z=3
: 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
rank=3 nullity=2
: (2)Find a basis for the colum space of A
[1 0 -2 0]^T [0 -1 -1 3]^T [0 3 3 -12]^T
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