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Let A be an m X n matrix and let R be the reduced row echelon form of A. Suppose that R has n k rows of zeroes_ Select all statements that are true. The span of the...

Question

Let A be an m X n matrix and let R be the reduced row echelon form of A. Suppose that R has n k rows of zeroes_ Select all statements that are true. The span of the columns of R is the same as the span of the columns of A dim(Row(A) ) dim(Null( A) ) rank( A) =m Row( A) is a subspace of Rm None of the above

Let A be an m X n matrix and let R be the reduced row echelon form of A. Suppose that R has n k rows of zeroes_ Select all statements that are true. The span of the columns of R is the same as the span of the columns of A dim(Row(A) ) dim(Null( A) ) rank( A) =m Row( A) is a subspace of Rm None of the above



Answers

Let $A$ be an $m \times n$ matrix. Show that the columns of $A$ are linearly independent if and only if $A^{T} A$ is invertible.


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