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math115: fix col space definition

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eggy 2022-11-18 18:09:39 -05:00
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docs/ce1/math115.md
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@ -654,7 +654,7 @@ $$\text{Null}(A) = \{\vec x\in\mathbb R^n | A\vec x = \vec 0\}$$
Its dimension is equal to the number of free vectors in RREF.
The **column space** of a matrix is the set of all linear combinations of its columns, which can be found by taking a linearly independent subset of the matrix (non-free vectors in RREF).
The **column space** of a matrix is the set of all linear combinations of its columns, which can be found by taking a linearly independent subset of the matrix (the **original vectors** of the non-free vectors in RREF).
$$\text{Col}(A) = \{A\vec x |\vec x\in\mathbb R^n \} = \text{Span}\{\vec a_1, \vec a_2, ..., \vec a_n\}$$