[123]⋅[456]=1⋅4+2⋅5+3⋅6\left[ \begin{array}{c} 1 & 2 & 3 \end{array}\right]\cdot\left[ \begin{array}{ccc} 4 \\ 5 \\ 6 \end{array}\right]= 1\cdot4 + 2\cdot5 + 3\cdot6

    [123]⋅[456]=[1⋅41⋅51⋅62⋅42⋅52⋅63⋅43⋅53⋅6]\left[ \begin{array}{c} 1 \\ 2 \\ 3 \end{array}\right]\cdot\left[ \begin{array}{ccc} 4 & 5 & 6 \end{array}\right]=\left[ \begin{array}{c} 1\cdot4 & 1\cdot5 & 1\cdot6 \\ 2\cdot4 & 2\cdot5 & 2\cdot6 \\ 3\cdot4 & 3\cdot5 & 3\cdot6 \end{array}\right]

    [123]⋅[475869]=[1⋅4+2⋅5+3⋅61⋅7+2⋅8+3⋅9]\left[ \begin{array}{c} 1 & 2 & 3 \end{array}\right]\cdot\left[ \begin{array}{ccc} 4 & 7\\ 5 & 8\\ 6 & 9 \end{array}\right]=\left[ \begin{array}{ccc} 1\cdot4+2\cdot5+3\cdot6 & 1\cdot7+2\cdot8+3\cdot9 \end{array}\right]

    [123456]⋅[710811912]=[1⋅7+2⋅8+3⋅91⋅10+2⋅11+3⋅124⋅7+5⋅8+6⋅94⋅10+5⋅11+5⋅12]\left[ \begin{array}{c} 1 & 2 & 3\\ 4 & 5 & 6 \end{array}\right]\cdot\left[ \begin{array}{ccc} 7 & 10\\ 8 & 11\\ 9 & 12 \end{array}\right]=\left[ \begin{array}{ccc} 1\cdot7+2\cdot8+3\cdot9 & 1\cdot10+2\cdot11+3\cdot12\\ 4\cdot7+5\cdot8+6\cdot9 & 4\cdot10+5\cdot11+5\cdot12 \end{array}\right]