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NCERT Solutions for Class 10 Maths Chapter 12 Areas Related to Circles Ex

In every question of 12th Maths Chapter 3 Matrix, the explanation of each step is given. The step by step solutions for plus two Maths is given with video ch 12 maths class 10 ex 12.3 an and PDF file format. We will definitely rectify. The arrangement of real numbers in a rectangular array enclosed in brackets as [] or is known as cn Matrix Matrices is plural of matrix.

Matrix operations are used in electronic physics, computers, budgeting, cost estimation, analysis and experiments. They are also used in cryptography, modern psychology, genetics, industrial management.

In general an m x n matrix is matrix having m rows and n columns. There may be any number of rows and any number of columns in a matrix.

If there are m rows and n columns in matrix A, its order is m x n and it is read as an m x n matrix. Theorems of invertible matrices. Matrix ch 12 maths class 10 ex 12.3 an a latin word.

Originally matrices are used for solutions of simultaneous linear equations. Carl Friedrich Gauss � also gave the method to solve simultaneous equations by matrix method. Matrix The arrangement of real numbers in a rectangular array enclosed in brackets as [] or is known as a Matrix Matrices is plural of matrix. Order of a Matrix There may be any number of rows and any number of columns in a matrix. Types of Matrices Row matrix: A row matrix has only one row am any number of columns.

Column matrix: A column matrix has only one column but any number of rows. Square matrix: A square matrix has the number of column equal to the number of rows. Rectangular Matrix: A matrix is said to be a rectangular matrix if the number of rows is not equal to the number of columns. Diagonal matrix: If in math square matrix has all elements 0 except principal diagonal elements, it is called diagonal matrix. Scalar Matrix: Qn diagonal matrix is said to be a scalar matrix if all the elements in its principal diagonal are equal to some non-zero constant.

Zero or Null matrix: If all elements of a matrix are zero, hc the matrix is known as zero matrix and denoted by O. Unit or Identity matrix: If in a square matrix has all elements 0 and each diagonal elements are non-zero, it is called identity matrix and denoted by I. Equal Matrices: Two matrices are said to be ch 12 maths class 10 ex 12.3 an if they are of the same order and if their corresponding elements are equal.

Properties of Matrices When a matrix is multiplied by a scalar, then each of its element is multiplied by the same scalar. Additive identity is a zero matrix, which when added to a given matrix, gives the same given matrix, i. If A and B are two matrices of order m ch 12 maths class 10 ex 12.3 an p and p x n respectively, then their product will be a matrix C of order m x n.

Theorems of invertible matrices Theorem 1: Every invertible matrix possesses a unique inverse. Theorem 2: A square matrix is invertible iff it is non-singular. Historical Facts! Important Questions on 12th Maths Chapter 3 If a matrix has 24 elements, what are the possible orders it can have?

What, if it has 13 elements? Determinants �.

Main point:

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All questions are ordered easy to difficult. That means, easiest question is in the beginning and the more difficult question is at the end. On signing up you are confirming that you have read and agree to Terms of Service.

In this chapter, we will Revise our concepts about Area and Perimeter of Circle , and do some questions Then, we will see what arc , sector and segment of a circle is We will learn the formula for length of an arc and Area of sector Then, using Area of sector and Area of triangle formulas, we find Area of Segment We do some questions where different figures are combined, and we need to find their area and perimeter Click on an exercise link below to learn from the NCERT Book way.

Or you can also learn from Teachoo way, click on any concept below Concept Wise to get started. Click on any link below to start studying the chapter. Serial order wise Ex Ex Area of sector of circle.

Area of segment of circle and length of arc. There is no new formula or concepts in this exercise. The questions area based on multiple figures, such as sectors and quadrants, quadrant and segments, combination of two segments or triangle and segments, etc. There may be more ways to solve these questions depending the given conditions. Questions number 16 is similar to Example number 6, otherwise we can find the required area by dividing it into two sectors just as done above in the solutions.

All the questions in this exercise are based on simple applications of areas of triangles, sectors, segments, circles, square, quadrants, etc. The questions are in the form of the combinations of two or more figures.

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