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Math Help - Linearly independent rows

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    Linearly independent rows

    Let A be an n x n matrix. How do you show that the rows of A are linearly independent if and only if the columns of A span R^{n}?
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  2. #2
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    Quote Originally Posted by antman View Post

    Let A be an n x n matrix. How do you show that the rows of A are linearly independent if and only if the columns of A span R^{n}?
    the rows of A are linearly independent iff the columns of A^T are linearly independent iff A^T is invertible iff A is invertible iff the columns of A are linearly independent iff the columns of A span \mathbb{R}^n.
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