1 Introduction
- Gilbert Strange page
- Notes by Gilbert Strang
- A good way to think about multiplication is thinking about the "L" shape.
2 Questions
2.1 Solution 1.1
\(x_1w_1 + x_2w_2 + x_3w_3 = \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}\)
Give the values of \(w_1\), \(w_2\) and \(w_3\), the only way it can give a zero vector is if the three vectors lie in a origin.
2.2 Solution 1.2
\(\begin{bmatrix} 1 && 2 && 0 \\ 2 && 0 && 3 \\ 4 && 1 && 1 \end{bmatrix} \begin{bmatrix} 3 \\ -2 \\ 1 \end{bmatrix}\)
\(= 3 \begin{bmatrix} 1 \\ 2 \\ 4 \end{bmatrix} - 2 \begin{bmatrix} 2 \\ 0 \\ 1 \end{bmatrix} + 1 \begin{bmatrix} 0 \\ 3 \\ 1 \end{bmatrix}\)
\(= \begin{bmatrix} 3 \\ 6 \\ 12 \end{bmatrix} - \begin{bmatrix} 4 \\ 0 \\ 2 \end{bmatrix} + \begin{bmatrix} 0 \\ 3 \\ 1 \end{bmatrix}\)
\(= \begin{bmatrix} -1 \\ 9 \\ 11 \end{bmatrix}\)
2.3 Solution 1.3
It is true.