learning discrete variable

We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio..

We have seen the application of matrices and determinants in solving system of linear equation with three unknown variables. Matrices and determinants are also widely used in solving large system of linear equation. Some of these methods are Gauss-elimination method, Gauss-Jordan method e..

The above discussion leads to find the solution of a system of linear equations in two variables by using Cramer's rule. Cramer's rule suggests the use of determinants to solve a system of linear equations. Let us denote a 1 b 2 - a 2 b 1 (Denominators of x and y in (4) and (5)) as the de..

Question: Find n. Answer: i) ii) \ n = 8..

Question: Answer: i) ii) iii) ..

Question: Answer: ..

Question: Answer: ..

Question: Answer: ..

Question: Prove that the number of ways in which (m+n) dissimilar things can be divided into two groups containing m and n Answer: If we select m things out of (m+n) things, then n things are left out . Then, this gives (m+n) that can be divided into two groups containing m and n thin..

Question: Answer: = 5 + 10 + 10 + 5 + 1 = 31 = RH..