Matrix

Description:

• A collection of vectors in rows or columns

Matrix Addition/Subtraction:

• Must have the same size
• Match element by element
• Resulting to a new matrix of same size

Multiplication:

• Multiply with a scalar: $k\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)=\left(\begin{array}{cc}ka& kb\\ kc& kd\end{array}\right)$
• Multiply with another matrix:
  • Nb of columns in first matrix(top, mid, bot) must be same as rows in second matrix(left, center, right)
  • Remember: row times column
  • Generally, $AB\ne BA$
• $A^m{A}^n=A^n{A}^m=A^{m+n}$
• $(AB)CD=A(BC)D=AB(CD)$

Division:

• By Inverse

Denotes system of equations:

Zero matrix:

• $0_{22}=\left(\begin{array}{cc}0& 0\\ 0& 0\end{array}\right)$