Recent content by Alchemista

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    Undergrad Can This Matrix Represent a Linear Transformation?

    A matrix is a linear transformation expressed with respect to a basis for the source space and the target space. Given a linear transformation T:\mathbb{F}^n \to \mathbb{F}^m, the corresponding matrix written with respect to a basis \alpha for the source space and a basis \beta for the...
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    Undergrad Why is the term 'norm' used instead of 'absolute value' in vector spaces?

    Absolute value is the usual norm for \mathbb{R}. The euclidean norm is the usual norm for \mathbb{R}^n While the euclidean norm is sometimes written using the same notation as absolute value, it is not the same thing. Furthermore, in the abstract a norm is not necessarily the euclidean norm...
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    Undergrad Determining if a vector b is a linear combination of vectors a1,a2,a3

    You've misinterpreted the results of the row reduction. First let's start with the result: \left[ \begin {array}{cccc} 1&0&5&2\\ -2&1&-6&-1 \\ 0&2&8&6\end {array} \right] \to \left[ \begin {array}{cccc} 1&0&5&2\\ 0&1&4&3 \\ 0&0&0&0\end {array} \right] So the coefficients of a...