Are the number of vertices, number of sides, and number of angles in a..
Are the number of vertices, number of sides, and number of angles in a triangle equal? => No or Yes..
Geometrical representation of a Complex number, Argand diagram
>The absolute values of z 1 , z 2 and z 1 + z 2 are geometrically given by We know that the sum of any two sides of a triangle is greater than the third. Hence, in D ORP, we have with the equality holding only when O, P, Q are lying in a straight line. That is why this..
>The absolute values of z 1 , z 2 and z 1 + z 2 are geometrically given by We know that the sum of any two sides of a triangle is greater than the third. Hence, in D ORP, we have with the equality holding only when O, P, Q are lying in a straight line. That is why this..Matrices and Determinants
Summary - A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital letter. Two matrices are said to be comparable..
Argand diagram of the qth roots of a Complex number
All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude q /q and others are uniformly spaced around the circle separated from others by an angle 2p ..
Argand diagram of the qth roots of a Complex number
All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude and others are uniformly spaced around the circle separated from others by an angle..
All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude and others are uniformly spaced around the circle separated from others by an angle..Example:
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...
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...Some important results
Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then ad = bc This property is..
Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then ad = bc This property is..Equal Sets
Two sets A and B are said to be equal if and only if they contain the same elements i.e. if every element of A is in B and every element of B is in A. We denote the equality by A = ..
Equality of Matrices
Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6...
Two matrices are said to be equal if they have the same order and their corresponding elements are equal. e.g., then a = 1, b = 2, c = 3, d = 4, e = 5 and f = 6...Equality of Matrices
If two matrices have their corresponding elements equal, then they are called equal matrices. If then a = p, b = q, c = r and d = s. a = 7, b = 9, c = 3. (i) Two equal matrices are exactly the same. (ii) If rows are changed into columns and columns into rows, we get a ..
If two matrices have their corresponding elements equal, then they are called equal matrices. If then a = p, b = q, c = r and d = s. a = 7, b = 9, c = 3. (i) Two equal matrices are exactly the same. (ii) If rows are changed into columns and columns into rows, we get a ..See what our Users say :
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