11th samacheer maths solutions எல்லாம் ஒரே இடத்தில் இங்கு நீங்கள் பெற்றுக்கொள்ளலாம். students க்கு எந்தமாதிரி சொல்லிக்கொடுத்தால் புரியும் என்று நங்கள் ஆராய்ச்சி செய்து ஒரு புது முறையில் உங்களுக்காக வழங்குகின்றோம்.

11th samacheer maths students க்கு எளிதில் புரியும் வகையில் maths solution ஐ நங்கள் board மூலம் தெளிவாக்குகின்றோம்.

உங்களுக்கு இந்த 11 maths solutions புடித்திருந்தால் நீங்கள் உங்கள் நண்பர்களுக்கு இங்கு share செய்யவும்.

Matrices and Determinants are one of the oldest concepts in the history of Mathematics. It has traces in the 2nd and 4th century BC. But the concepts were well developed in the 17th Century. The need for matrices and determinants came when the mathematicians tried to solve the problem related to multiple simultaneous linear equations. It has traces to the Babylonians era and they have created some of the clay tablets with these matrices which are still preserved.

Matrices assists us to solve multiple linear equations using a simple methods. This has wider applications in the normal life. In modern application, the matrices are widely used in analytics to solve complex problems using computer. The analytics problems includes prediction and prescriptive model developments using matrices.

Surprisingly the word matrix is coined by a lawyer in association with a mathematician in the 17th century. Since the concept of matrix is invented this had a powerful application among the concepts of mathematics.

We can see matrixes in normal life. In terms of organising 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 quadratic form makes the basis for the term determinants. This was coined by Gauss in 17th Century. Further the concept of determinants was expanded by another famous mathematician Cauchy.

Using matrices we can write the coefficient of the linear equation. This helps us to solve multiple linear equations together. In data is represented in excel spread sheet normally as a matrices and it has wider application in almost all corporates and educational institutions. Many of the dashboards developed for management decision making and operational analysis are also in a matrices format with tables that comprise of rows and columns. For example, population across different states in india for the past 10 years can easily be depicted in the form of a table with years in the columns and states in the rows.

Matrices is a rectangular array of elements distributed in two dimentional as rows and columns. Usually we put a square bracket covering these rows and columns to indicate that whatever elements within this bracket forms a matrix. The elements of matrices can either be a constant, variable or functions.

If the matrices is having A number of rows and B number of columns then the size of the matrices is determined by multiplication of A * B. For example, if a matrices is having 10 rows and 5 columns then the size of the matrices is 50.

The matrices that have only a single row, it is called as row matrices.

The matrices that have only a single column is called as column matrices.

The zero matrices is a type of matrices where in all the elements of the matrices are 0. There are different names for the zero matrices. It is also called as Void Matrix or null Matrix.

The square matrices are the ones that have equal number of row elements and column elements.

In a square matrix we can have principal diagonal, that is represented by elements that falls in the diagonal line. There are different names for the principal diagonal. It is also called as diagonal , main diagonal, or leading diagonal elements.

If all the elements in the diagonal are equal in a square matrix then the matrix is called as scalar matrix.

Unit matrix are the ones which has values only in the diagonal and the rest of the elements are all zero. In the diagonal elements all the elements will have value as 1.

The square matrix can have a special type of matrix called as triangular matrix. In the square matrix if all the elements in the bottom of the diagonal are zero then it is called as the triangular matrix.

When we have to compare two matrices, we can say that both are equal only if all the elements in the matrices are equal. And all the elements are positioned in the same position in both the matrices. If any of the element is not same or not in the same order then it is called as unequal matrices.

We can do algebric operations on Matrices such as addition, multiplication, subtraction. Only the division of two matrices is not possible. Even for addition, subtraction and multiplication there are certain prerequisite to be satisfied before we perform the operations.

If we have to multiple a matrix with a constant (called as scalar), then we need to multiply all the elements of the matrices with the scalar element. For example, if the scalar is K and if we multiply a matrix with K then we need to multiple each of the element of the matrix with K.

We can do addition and subtraction of matrices if both the matrices are having same number of rows and columns. In that case the addition of matrix A with matrix B indicates A+B of each of the elements of the matrices. Similarly the subtraction of Matrix A with matrix B indicates A-B of each of the elements of the matrices. When the question asks for addition or subtraction of matrices we need to first validate whether the number of rows and columns of one matrix is same as the number of rows and columns in the other matrix. If not, we need to mention in the result that such an addition or subtraction is not possible. Students have to be careful about such questions as it can trick students asking to add or subtract such matrices which is not possible.

We can multiple two matrices only if the number of columns of A is equal to number of rows of B. For example, if a matrix is having 10 columns we can then try to multiple with another matrix with 10 columns it is not possible. For the multiplication to be possible we need to have 10 columns in the first matrix and 10 rows in the 2nd matrix. Here 10 is just an example. The multiplication will work even for other numbers only if the number of rows and columns should tally.