discrete mathematics solution

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 solution..

A system of linear equations is said to be consistent if it has a solution. This means that the solution satisfies all the equations in the system simultaneously. If a system of linear equations has no solution, then it is said to be inconsiste..

If D = 0 and all D 1 , D 2 and D 3 are zeros, this system has either infinite solution or no solution. In this case, put x = k(y = k or z = k), in any two of the equations, find y and z in terms of k. Substitute these values of x, y and z in terms of k, in the third equation...

If D = 0 and D 1 , D 2 and D 3 are not all zero, then the system is inconsistent, that is the system has no solution..

A - 1 does not exist But if (adj A) B = 0, then the system is consistent with infinite number of solutions or has no solution. the system is inconsistent i.e., it has no solution..

= (14 - 12) - (7 - 3) + (4 - 2) = 2 - 4 + 2 = 0 The system may have infinite number of solutions or no solution. Put x = k in (1) and (2) and solve y + z = 6 - k 2y + 3z = 14 - k. Solving the above two equations, we have z = k + 2 and y = 4 - 2k When x = k, substituting t..

Using determinants, find the area of triangle whose vertices are (2, -7), (1, 3), (10, 8). Solution: (x 1 , y 1 ) = (2, -7) (x 2 , y 2 ) = (1, 3) (x 3 , y 3 ) = (10, 8) Area of the triangle = -47.5 Since area has to be a positive quantity, it is given by 47.5 sq.uni..

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 respectively the first c..

Note that we can also evaluate the determinant D 1 , D 2 and D 3 directly without using the properties of determinant. The solution of the system is given by It is important to mention here the consistency and inconsistency of a system of linear equations with three unknown..

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