1. Simple Matrix Multiplication

If you have the vector [1,0,0,0] and multiply it by the row vector [0, f_2, 0, f_4], I understand the result will be a 4x4 matrix, but I'm not sure exactly how to compute it and how you end up with [0, f_2, 0, f_4] in the top row and the rest of the entries 0.

2. Originally Posted by flash101
If you have the vector [1,0,0,0] and multiply it by the row vector [0, f_2, 0, f_4], I understand the result will be a 4x4 matrix, but I'm not sure exactly how to compute it and how you end up with [0, f_2, 0, f_4] in the top row and the rest of the entries 0.
$\displaystyle \underbrace{\left[ \begin{array}{cccc} 1&0&0&0 \end{array} \right]}_{1\times 4} \underbrace{\left[ \begin{array}{c}0\\a\\0\\b \end{array}\right]}_{4\times 1} = \overbrace{[0]}^{1\times 1}$

$\displaystyle \underbrace{\left[ \begin{array}{c}0\\a\\0\\b \end{array}\right]}_{4\times 1}\underbrace{\left[ \begin{array}{cccc} 1&0&0&0 \end{array} \right]}_{1\times 4} = \overbrace{\left[\begin{array}{cccc}0&0&0&0\\a&0&0&0\\0&0&0&0\\b&0& 0&0 \end{array} \right]}^{4\times 4}$