[考古] 線性代數/林秀峰/97上期中考

[XX9 ( 佛曰: ....)]

※ [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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