Matrices and Logarithms

Addition

Add corresponding entries. Matrices must be same size.

Scalar Multiplication

Multiply every entry by the scalar.

Matrix Multiplication

Row × column. $(m \times n) \cdot (n \times p) = (m \times p)$.

$\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} 5 \\ 6 \end{pmatrix} = \begin{pmatrix} 17 \\ 39 \end{pmatrix}$

Determinant (2×2)

$\det\begin{pmatrix} a & b \\ c & d \end{pmatrix} = ad - bc$

$\log_a b = c$ means $a^c = b$.

Log Rules

• $\log(xy) = \log x + \log y$
• $\log(\frac{x}{y}) = \log x - \log y$
• $\log(x^n) = n\log x$
• $\log_a a = 1$, $\log_a 1 = 0$

Example

$\log_2 32 = 5$ because $2^5 = 32$.

$\log_3 \frac{1}{9} = -2$ because $3^{-2} = \frac{1}{9}$.