Posts for Tag: Algebra

Permutation and Combinations – HSC Math

$\n!=\n(\n-1)(\n-2) … … 3.2.1$ i. $^\n\P_\r=\n(\n-1)(\n-2) … … (n-r+1)$ ii. $^\n\P_\n=\n!$ iii. $^\n\P_\r={\n!}/{(\n-\r)!}$ $^\n\C_\r=^\n\C_{\n-\r}={\n!}/{{\n!}(\n-\r)!}$ $^\n\C_\r+^\n\C_{\r-1}=^{\n+1}\C_\r$ Number of combination of $\n$ different items taken at least one at a time is $2^n-1$. i. If $\n$ items are arranges in a cyclic order, number of permutation is $(\n-1)!$ ii. If teh cycle can be flipped, number ofRead More

Matrix and Determinant Formulas – HSC Math

Let A is a matrix with m row and n column. Then the dimension of a matrix A is m x n. Let A and B are matrices with dimension m x n and p x q respectively. Then multiplication of A and B, i.e. A.B is possible if and only if n=p. if $A=[\tableRead More