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Math Help - line equations

  1. #1
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    line equations

    line equations Ax=b,where A is an m*n matrix, x is an n*1 matrix, b is an m*1matrix ,m<n. Each element in A,x,b is real . I want to know under what condition the x is bounded , which is also mean each element in x is lower than a real positive number and larger than 0.
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  2. #2
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    Dear xhxchina,

    I will try to help. But can you please explain me about what you mean by "x is bounded".
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  3. #3
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    Quote Originally Posted by Sudharaka View Post
    Dear xhxchina,

    I will try to help. But can you please explain me about what you mean by "x is bounded".
    x is a n*1 matrix, every element in x is a real number. the x is bounded means every element in x is smaller than a finite real positive number and greater than zero.
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  4. #4
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    adding a condition

    If the problem is too difficult ,I will add a condtion on matrix A,
    Rank(A)=m, I want to know under what condition matrix x is bounded.
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  5. #5
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    Quote Originally Posted by xhxchina View Post
    line equations Ax=b,where A is an m*n matrix, x is an n*1 matrix, b is an m*1matrix ,m<n. Each element in A,x,b is real . I want to know under what condition the x is bounded , which is also mean each element in x is lower than a real positive number and larger than 0.
    If A and b are specific matrices, then x is a specific matrix and, of course, is "bounded". So you must mean that A and/or b are variable. Are they themselves bounded?
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  6. #6
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    Quote Originally Posted by HallsofIvy View Post
    If A and b are specific matrices, then x is a specific matrix and, of course, is "bounded". So you must mean that A and/or b are variable. Are they themselves bounded?
    A and b isn't variables, they are specific.
    line equations Ax=b,where A is an m*n matrix, x is an n*1 matrix, b is an m*1matrix ,m<n, Rank(A)=m. Each element in A,b is real,so A and b is specific . the equations has infinite solutions x,
    Then I want to know under what condition the x is bounded.
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