Example 1:
Using matrix method solve the following systems of linear equations 2x - y + z = -3 3x - z = - 8 2x + 6y ..
Case I:
Pre-multiply by A - 1 , \ A - 1 (AX) = A - 1 B \ (A - 1 A) X = A - 1 B \ I X = A - 1 B or X = A - 1 B This is the matrix method to solve the equations. However, ..
Pre-multiply by A - 1 , \ A - 1 (AX) = A - 1 B \ (A - 1 A) X = A - 1 B \ I X = A - 1 B or X = A - 1 B This is the matrix method to solve the equations. However, ..Consistency of a system of linear equation
If a system of linear equations has at least one solution, then the system is called consistent, otherwise it is called inconsistent. Solve the system of linear equations (1) by using method of elimination as studied earlier Multiplying the first equation by a 2 and ..
If a system of linear equations has at least one solution, then the system is called consistent, otherwise it is called inconsistent. Solve the system of linear equations (1) by using method of elimination as studied earlier Multiplying the first equation by a 2 and ..Matrices and Determinants Summary
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing resp..
The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from D by replacing resp..Question 1
or n < 2n Multiplying the above terms of both sides respectively, we get Multiplying both sides by n!, we get From (1) and (2), we g..
or n < 2n Multiplying the above terms of both sides respectively, we get Multiplying both sides by n!, we get From (1) and (2), we g..Corollary 1:
If we put r = n in the above formula, the..
If we put r = n in the above formula, the..Question 1
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: 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..Note 1:
Only a square matrix can have its invers..
Discrete Mathematics - Test Questions I
Question 1 - Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done ..
Question 1 - Question: From a class of 32 students, 4 are to be chosen for a competition. In how many ways can this be done? Answer: We are to select 4 students from 32. This selection can done ..See what our Users say :
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