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Key Equations

(M5-1)

(\begin{matrix} a \\ b \\ c \end{matrix}) \times (\begin{matrix} d & e \end{matrix}) = (\begin{matrix} a d & a e \\ b d & b e \\ c d & c e \end{matrix})

$(\begin{matrix} a \\ b \\ c \end{matrix}) \times (\begin{matrix} d & e \end{matrix}) = (\begin{matrix} a d & a e \\ b d & b e \\ c d & c e \end{matrix})$

Multiplying matrices.

(M5-2)

(\begin{matrix} a & b \\ c & d \end{matrix}) \times (\begin{matrix} e & f \\ g & h \end{matrix}) = (\begin{matrix} a e + b g & a f + b h \\ c e + d g & c f + d h \end{matrix})

$(\begin{matrix} a & b \\ c & d \end{matrix}) \times (\begin{matrix} e & f \\ g & h \end{matrix}) = (\begin{matrix} a e + b g & a f + b h \\ c e + d g & c f + d h \end{matrix})$

Multiplying $2 \times 2$ $2 \times 2$ matrices.

(M5-3)

A \times A^{- 1} = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix})

$A \times A^{- 1} = (\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix})$

The identity matrix.

(M5-4)

{(\begin{matrix} a & b \\ c & d \end{matrix})}^{- 1} = (\begin{matrix} \frac{d}{a d - c b} & \frac{- b}{a d - c b} \\ \frac{- c}{a d - c b} & \frac{a}{a d - c b} \end{matrix})

${(\begin{matrix} a & b \\ c & d \end{matrix})}^{- 1} = (\begin{matrix} \frac{d}{a d - c b} & \frac{- b}{a d - c b} \\ \frac{- c}{a d - c b} & \frac{a}{a d - c b} \end{matrix})$

The inverse of a $2 \times 2$ $2 \times 2$ matrix.

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Table of Contents for Key Equations

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Table of Contents for
Key Equations