Matrix Product (Conventional)/Examples/Arbitrary 3

Example of (Conventional) Matrix Product

$\begin {bmatrix} 2 \\ 0 \\ 6 \end {bmatrix} \begin {bmatrix} 5 & 3 & 1 \end {bmatrix} = \begin {bmatrix} 10 & 6 & 2 \\ 0 & 0 & 0 \\ 30 & 18 & 6 \end {bmatrix}$

Proof

\(\ds \begin {bmatrix} 2 \\ 0 \\ 6 \end {bmatrix} \begin {bmatrix} 5 & 3 & 1 \end {bmatrix}\)

\(=\)

\(\ds \begin {bmatrix} 2 \times 5 & 2 \times 3 & 2 \times 1 \\ 0 \times 5 & 0 \times 3 & 0 \times 1 \\ 6 \times 5 & 6 \times 3 & 6 \times 1 \end {bmatrix}\)

\(\ds \)

\(=\)

\(\ds \begin {bmatrix} 10 & 6 & 2 \\ 0 & 0 & 0 \\ 30 & 18 & 6 \end {bmatrix}\)

$\blacksquare$

Sources

• 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 29$. Matrices