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...
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...
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...