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 repl..
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 repl..Multiplication of Matrices
Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matrices can be multiplied by usin..
Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix. Two matrices can be multiplied by usin..Introduction to Permutations and Combinations
Introduction - Arrangement and selection of objects are the central ideas of this chapter on permutations and combinations. They are widely applied in solving problems of probability, genetic engineering and life scienc..
Matrices, Determinants Conclusion
Conclusion - 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..
Permutations and Combinations
Introduction - Arrangement and selection of objects are the central ideas of this chapter on permutations and combinations. They are widely applied in solving problems of probability, genetic engineering and life science..
Example:
Solve the system of linear equations. x +2y + 3z = 6 2x + 4y + z = 7 3x + 2y + 9z = 14 using Cramer's rul..
Conclusion
In this chapter, we have seen how arranging numbers in orderly rows and columns under the guise of Matrices and Determinants, has helped to solve linear equations or find the area of a triangle. There are in fact other much wider applications in Science and Engineering and other fi..
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, ..Step 2:
Solve f '(x) = 0 to get the critical values for f (x). Let these values be a, b, c. These are the points of maxima or minima. Arrange these values in ascending ord..
Step 2:
Find the co-ordinates of each vertex of the feasible region. These co-ordinates can be obtained from the graph or by solving the equation of the line..
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