Introduction to Matrices
Intro to Matricies
- A Matrix is an array of (usually numbers) set out in brackets.
- The dimentions of a matrix is the size. Shows the number of rows and columns (in that order).
For example: $$\begin{pmatrix}
2 & -7 & 6&7& 2\
2 & 9 & 4 & 9 &11
\end{pmatrix}$$
has the dimensions \(5\times2\)
- We use bold capital letters to define matricies.
- \(\mathbf{A}=\) a matrix
Adding matricies
- \(\begin{pmatrix} 4& 8 \\6 &1 \end{pmatrix} +\begin{pmatrix} -5& 3 \\ 6& 13\end{pmatrix} =\begin{pmatrix}-1 &11 \\12 &14 \end{pmatrix}\)
- You add or subtract the elements of the corresponding places in the matrix.
Subtracting matricies
- \(\begin{pmatrix}q &5 \\9 & t\end{pmatrix}-\begin{pmatrix} 4&8 \\-3 & 0\end{pmatrix}=\begin{pmatrix}q-4 &-3 \\12 & t\end{pmatrix}\)
- Using these rules you can add and subtract variables in matricies.
Scalar Multiplication
- \(\mathbf{A}=\begin{pmatrix}5 &-4 \\2w & 5\end{pmatrix}\)
- \(2\mathbf{A}=\begin{pmatrix} 10&-8 \\4w & 10\end{pmatrix}\)
Special Matricies
- A square matrix has the same number of rows as columns.
$$\begin{pmatrix}
1 & 1 \
1&1
\end{pmatrix}$$
- A zero matrix is where all the elements are 0.
\(\(\mathbf{0}=\begin{pmatrix} 0 &0 &0 \\ 0& 0 & 0 \\ 0 & 0 &0 \end{pmatrix}\)\)- An identity matrix is a matrix which has 1's in the leading diagonal, but zeros everywhere else.
\(\(\mathbf{I}=\begin{pmatrix} 1& 0 &0 \\ 0& 1 &0 \\ 0& 0 & 1 \end{pmatrix}\)\)