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Matrix In  mathematics , a  matrix  (plural:  matrices ) is a  rectangular   array  of  numbers ,  symbols , or  expressions , arranged in  rows  and  columns . For example, the dimensions of the matrix below are 2 × 3 (read "two by three"), because there are two rows and three columns: {\displaystyle {\begin{bmatrix}1&9&-13\\20&5&-6\end{bmatrix}}.} Provided that they have the same size (each matrix has the same number of rows and the same number of columns as the other), two matrices can be  added  or subtracted element by element (see  Conformable matrix ). The rule for  matrix multiplication , however, is that  two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second  (i.e., the inner dimensions are the same,  n  for an ( m × n )-matrix times an ( n × p )-matrix, resulting in an ( m × p )-matrix...

Differentiation Differentiation allows us to find rates of change. For example, it allows us to find the rate of change of velocity with respect to time (which is acceleration). It also allows us to find the rate of change of x with respect to y, which on a graph of y against x is the gradient of the curve. There are a number of simple rules which can be used to allow us to differentiate many functions easily. If y = some function of x (in other words if y is equal to an expression containing numbers and x's), then the  derivative  of y (with respect to x) is written dy/dx, pronounced "dee y by dee x" . Differentiating x to the power of something 1) If y = x n , dy/dx = nx n-1 2) If y = kx n , dy/dx = nkx n-1 (where k is a constant- in other words a number) Therefore to differentiate x to the power of something you bring the power down to in front of the x, and then reduce the power by one. Examples If y = x 4 , dy/dx = 4x 3 If y = 2x 4 , d...