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math115: correct row space definition

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eggy 2022-11-13 21:12:52 -05:00
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@ -660,7 +660,7 @@ $$\text{Col}(A) = \{A\vec x |\vec x\in\mathbb R^n \} = \text{Span}\{\vec a_1, \v
Its dimension is equal to the rank of the matrix. Its dimension is equal to the rank of the matrix.
The **row space** of a matrix is the set of all linear combinations of its rows, which can be found by taking each row, excluding free vectors, from RREF. The **row space** of a matrix is the set of all linear combinations of its rows, which can be found by taking each non-zero row from RREF.
$$\text{Row}(A) = \{A^t\vec x | \vec x\in\mathbb R^n\} = \text{Span}\{\vec r_1, \vec r_2, ..., \vec r_m\}$$ $$\text{Row}(A) = \{A^t\vec x | \vec x\in\mathbb R^n\} = \text{Span}\{\vec r_1, \vec r_2, ..., \vec r_m\}$$