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Math Help - 3 x 6 matrix

  1. #1
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    3 x 6 matrix

    If B is a 3 x 6 matrix whose last column has all zeros, then the number of parameters in the general solution of the linear system with augmented matrix B is at most ______________?
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  2. #2
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    Re: 3 x 6 matrix

    If B is an augmented matrix, then the 6th column represents a solution vector, ie, you're trying to find what combinations of the five column vectors add up to the zero vector. That makes five variables ... in equation form each row will look something like this ...

    2x + y + 3w + 4z + 7u = 0

    ... with three equations (rows), the number of pivot columns cannot be greater than 3. So the number of non-pivot columns, which is equal to the number of parameters in the general solution is ...

    I'll check back later to see if you fill in the blank.
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