Thread: 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.

Dear xhxchina,

I will try to help. But can you please explain me about what you mean by "x is bounded".

Originally Posted by Sudharaka

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.

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.

Originally Posted by xhxchina

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?

Originally Posted by HallsofIvy

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.