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Math Help - Matrix - Gauss-Jordan

  1. #1
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    Exclamation Matrix - Gauss-Jordan

    please help me to solve this question



    For which values of ( a ) will the system of equations

    x+y=0

    x+2y+(a+3)z=0

    x+y+(a+1)z=a^2 - 1 ( a square minus 1 )

    has :

    1 - A unique non-zero solution
    2- No Solution
    3- A trivial solution
    4- infinitely many solutions

    please i need a little bit of explanation on that
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  2. #2
    MHF Contributor
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    Talking

    Quote Originally Posted by 7amooood View Post
    For which values of ( a ) will the system of equations

    x+y=0
    x+2y+(a+3)z=0
    x+y+(a+1)z=a^2 - 1

    has :

    1 - A unique non-zero solution
    2- No Solution
    3- A trivial solution
    4- infinitely many solutions
    Use what you've learned about solving systems of linear equations:

    For a system to have infinitely-many solutions, one of the lines in the system has to turn into all zeroes, after a sufficient number of row operations.

    For a system to have no solution, one of the lines has to reduce to something non-sensical, like "2 = 0".

    For a unique solution, you have to get single numerical values for each of x, y, and z.

    (I don't know how your book is defining a "trivial" solution in this context, but it might mean "everything is zero".)

    So do the row operations, trying to get the system into row-echelon or reduced-row-echelon form, and see where that leads!
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  3. #3
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    Thumbs up Thanks

    Thank you very much that helped me so much and i was able to figure out the answer for the question
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