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11 Samacheer Maths Solutions for 7.1.3 is given in a real board in a hand written format. This would be useful for students to understand the solution in easy and simple manner. The grasping power increases by reading the solution in a notes format. Hence we have given all the solution in volume 2 in this board format. Please share with your friends if you find this format useful.
One of the oldest concepts in mathematics is matrices and Determinants.There are traces in the 2nd and 4th century BC.The concepts were developed in the 17th Century.When mathematicians tried to solve a problem with multiple simultaneous linear equations they needed matrices and determinants.Some of the clay tablets made with the matrices that are still preserved are from the Babylonians era.
There are more applications in the normal life.In modern application the matrices are used to solve complex problems using a computer.Predicting and model developments using matrices are included in the analytics problems.A lawyer and a mathematician created the word matrix in the 17th century.The concept of matrix has a strong application in mathematics.
In terms of arranging cars in a parking area coconut trees in a farm land and storage of boxes in a storage area we can see matrices in common practise.The basis for the term depends on the form.This was invented by Gauss in the 17th century.The concept of determinants was expanded by another famous mathematician.The coefficients of linear equations can be written using matrices.
Data is represented in excel spread sheet as matrices and it is used in almost all corporates and educational institutions.Many of the dashboards developed for management decision making and operational analysis are in matrices format with rows and columns.A table with years in the columns and states in the rows can be used to show the population over the past 10 years.There are rows and columns in a rectangular array of elements.The brackets are usually put over the rows and columns to indicate that a matrix has been formed.
The size of the matrices is determined by the number of rows and columns in the matrix.If there are 10 rows and 5 columns the size of the matrices is 50.The matrices that only have one row are called row matrices.Column matrices are matrices with only one column.The zero matrices are a type of matrices where the elements of the matrices are not 0.
It is called a null matrix.The square matrices have the same number of elements.The elements that fall in the diagonal line are represented in a square matrix.There are many different names for the diagonal.It's also called main diagonal or leading diagonal elements.
The rest of the elements are all zero in the unit matrix which has values only in the diagonal.All elements will have a value of 1 in the diagonal elements.A triangular matrix is a special type of matrix.If all the elements in the bottom of the diagonal are zero it's called the triangular matrix.If all the elements in the matrices are equal we can say that the two matrices are not equal.
If any of the elements are not the same or not in the same order then they are called unequal matrices.Adding multiplication and subtracting are some of the algebric operations we can do.Only the division of two matrices is possible.There are certain things we need to be satisfied with before we do the operations.If we have to multiplication all the elements of the matrices with a single element we need to use a constant.
If the matrices have the same number of rows and columns we can add and subtract them.The addition of matrix A with matrix B shows A+B of the elements of the matrices.The A-B of each of the elements of the matrices is indicated by the subtraction of Matrix A with matrix B.If the number of rows and columns of one matrix is the same as the number of rows and columns in the other matrix we need to add or subtract the matrices.We need to mention in the result that adding or subtracting something is not possible.