math problem (linear algebra)

please provide the procedure....I will give more mark if you think 20 is not enough...however, I only have 100 marks left...please help me..

Question 4: Write the following system of linear equations in the form Ax =b and

solve it.

x−y + 4z = 17

x+3y+ = −11

−6y + 5z = 40.

.Question 6: The trace of a square matrix of order n, A = [aij ]1=<i,j=<n, is defined to

be the sum of main diagonal entries of A. That is Tr(A) = a11 +a22 +· · · ann. Prove

that if A and B square matrices of order n, then Tr(AB) = Tr(BA).

1 Answer

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    1 decade ago
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    x+3y+ = −11? 要加什麼z?

    2009-02-05 14:41:17 補充:

    Question 4:

    In the form of Ax = b:

    [1 -1 4][x] [17 ]

    [1 3 0 ][y]=[-11]

    [0 -6 5][z] [40 ]

    Solve:

    [1 -1 4 17]

    [1 3 0 -11]

    [0 -6 5 40]

    row2 = row1-row2

    [1 -1 4 17]

    [0 -4 4 28]

    [0 -6 5 40]

    row2 = row2/(-4)

    [1 -1 4 17]

    [0 1 -1 -7]

    [0 -6 5 40]

    row1 = row1+row2, row3 = row2*6+row3

    [1 0 3 10 ]

    [0 1 -1 -7]

    [0 0 -1 -2]

    row3 = row3/(-1)

    [1 0 3 10 ]

    [0 1 -1 -7]

    [ 0 0 1 2 ]

    row1 = row1-row3*3, row2 = row2+row3

    [1 0 0 4 ]

    [0 1 0 -5]

    [0 0 1 2 ]

    So, x = 4, y = -5, z = 2.

    (p.s. You can use inverse of A to solve this problem as well)

    Question 6:

    See part (a) of http://lrg103.zorpia.com/0/4945/31653147.2d1a12.jp...

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