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Thanks,

JL

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- Thread starter jeff1evesque
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- #1

- 312

- 0

Thanks,

JL

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Yes. Keep in mind that [tex]\det(A) = \det(A^{T})[/tex], hence every portion of the invertible matrix theorem automatically applies to the rows as well as the columns. You should come to see that there is a relationship between the row space and the column space of a matrix, along with the null space, called the rank-nullity theorem.

Note that the space spanned by the rows is different then the space spanned by the columns since row vectors live in a different vector space than the column vectors. (You will find that there is an isomorphism between the two spaces if the matrix is n x n.)

Note that the space spanned by the rows is different then the space spanned by the columns since row vectors live in a different vector space than the column vectors. (You will find that there is an isomorphism between the two spaces if the matrix is n x n.)

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