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Math Help - Determining linear dependence or independence from the row reduced matrix

  1. #1
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    Determining linear dependence or independence from the row reduced matrix

    If I have a matrix and make it into reduced row-echelon form, how can I determine whether the vectors that form the matrix are linearly independent or dependent?
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  2. #2
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    Echelon form of the matrix has its determinant = 1

    you want to know about linear dependence of vectors of a row reduced echelon form of a matrix
    if it could be reduced to echlon form then its cant be linearly dependent
    if vectors are linearly dependent then it cant be made into echelon form
    take an example and try urself
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  3. #3
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    Specifically, if, trying to row- reduce a matrix to reduced row-echelon form, you get an entire row of zeroes, the vectors are dependent. Otherwise, they are independent.
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  4. #4
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    Quote Originally Posted by HallsofIvy View Post
    Specifically, if, trying to row- reduce a matrix to reduced row-echelon form, you get an entire row of zeroes, the vectors are dependent. Otherwise, they are independent.
    Is it true that if we have all the columns leading, then it must be linearly independent.
    Linear dependence occurs when the entire row is zeroes (when trying to get into reduced row-echelon form)
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  5. #5
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    Linear dependence occurs when the entire row is zeroes (when trying to get into reduced row-echelon form).
    Correct.

    Is it true that if we have all the columns leading, then it must be linearly independent.
    What do you mean by "columns leading"?
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