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Math Help - Need help with a problem. Ax=b

  1. #1
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    Need help with a problem. Ax=b

    We just started class and our first HW problem over a chapter we haven't gotten to yet has me stumped.

    The instructor made this one up I believe, and the following is from the chalkboard;

    [1 2 0 1 3 | 4 ] is the reduced row echelon form if [A.b] for the eqn.
    [0 0 1 2 4 | -3] Ax=b. Find solution for x.
    [0 0 0 0 0 | 0 ]

    From what I can gather by reading ahead in the book is for an Ax=b situation the solution is given by x=A^-1 * b... or x equals the inverse of A times b. From what I have read, inverses can only be calculated from matrices that are square or nxn dimensions. Therefore, I am stumped.

    Any help is greatly appreciated, even if you just show me a general method, so I can solve it on my own.
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  2. #2
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    Quote Originally Posted by prometheos View Post
    We just started class and our first HW problem over a chapter we haven't gotten to yet has me stumped.

    The instructor made this one up I believe, and the following is from the chalkboard;

    [1 2 0 1 3 | 4 ] is the reduced row echelon form if [A.b] for the eqn.
    [0 0 1 2 4 | -3] Ax=b. Find solution for x.
    [0 0 0 0 0 | 0 ]

    From what I can gather by reading ahead in the book is for an Ax=b situation the solution is given by x=A^-1 * b... or x equals the inverse of A times b. From what I have read, inverses can only be calculated from matrices that are square or nxn dimensions. Therefore, I am stumped.

    Any help is greatly appreciated, even if you just show me a general method, so I can solve it on my own.
    It's going to have infinitely many solutions.
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  3. #3
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    Quote Originally Posted by prometheos View Post
    We just started class and our first HW problem over a chapter we haven't gotten to yet has me stumped.

    The instructor made this one up I believe, and the following is from the chalkboard;

    [1 2 0 1 3 | 4 ] is the reduced row echelon form if [A.b] for the eqn.
    [0 0 1 2 4 | -3] Ax=b. Find solution for x.
    [0 0 0 0 0 | 0 ]

    From what I can gather by reading ahead in the book is for an Ax=b situation the solution is given by x=A^-1 * b... or x equals the inverse of A times b. From what I have read, inverses can only be calculated from matrices that are square or nxn dimensions. Therefore, I am stumped.

    Any help is greatly appreciated, even if you just show me a general method, so I can solve it on my own.
    just write Ax=b as a system of equations and solve it: \begin{cases} x_1 + 2x_2 + x_4 + 3x_5=4 \\ x_3 + 2x_4 + 4x_5 =-3 \end{cases}. we have two equations and 5 variables.

    the solutions are: x_1=4-2x_2-x_4-x_5, \ x_3=-3-2x_4-4x_5. note that x_2, x_4, x_5 are free variables.
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  4. #4
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    Ah, I think I see now what my problem was. The wording of the question led me to believe it wasn't a simple solution. Go go new math class language. Thank you.
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