Matrix Product (Conventional)/Examples/Arbitrary 2

Example of (Conventional) Matrix Product

$\begin {bmatrix} 5 & 3 & 1 \end {bmatrix} \begin {bmatrix} 2 \\ 0 \\ 6 \end {bmatrix} = \begin {bmatrix} 16 \end {bmatrix}$

Proof

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

\(=\)

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

\(\ds \)

\(=\)

\(\ds \begin {bmatrix} 10 + 0 + 6 \end {bmatrix}\)

\(\ds \)

\(=\)

\(\ds \begin {bmatrix} 16 \end {bmatrix}\)

$\blacksquare$

Sources

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