Here you will learn subtraction of matrices with examples. Let’s begin – Subtraction of Matrices Let two matrices A and B of the same order, the subtraction of matrix B from matrix A is denoted by A – B and is defined as A – B = A + (-B). Note : If matrices are not […]
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Here you will what is matrix and definitions of different types of matrices with examples. Let’s begin – What is Matrix ? A set of mn numbers (real or imaginary) arranged in the form of a rectangular array of m rows and n columns is called an m \(\times\) n matrix (to be read as
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Here you will learn equality of matrices definition with examples. Let’s begin – Equality of Matrices Definition : Two matrice A = \([a_{ij}]_{m\times n}\) and B = \([b_{ij}]_{r\times s}\) are equal if (i) m = r i.e. the number of rows in A equals the number of rows in B. (ii) n = s i.e the
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Here you will learn scalar multiplication with matrices (multiplicaition of a matrix by a scalar ) and properties of scalar mutiplication. Let’s begin – Scalar Multiplication with Matrices Definition : Let \([a_{ij}]\) be an \(m\times n\) matrix and k be any number called a scalar. Then the matrix obtained by mutiplying every element of A by
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Here you will learn how to add matrix and properties of addition of matrices with examples. Let’s begin – Addition of Matrices Let A, B be two matrices, each of order \(m \times n\). Then their sum A + B is a matrix of order \(m \times n\) and is obtained by adding the correspoding
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Here you will learn addition theorem of probability for two and three events with statement and proof. Let’s begin – Addition Theorem of Probability For two events : If A and B are two events associated with a random experiment, then P(\(A \cup B\)) = P(A) + P(B) – P(\(A \cap B\)) Proof : Let S
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Here you will learn formula to find the distance of a point from a line with examples. Let’s begin – Distance of a Point from a Line The length of the perpendicular from a point \((x_1, y_1)\) to a line ax + by + c = 0 is |\(ax_1 + by_1 + c\over {\sqrt{a^2+b^2}}\)|. It
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Here you will learn how to find point of intersection of two lines with examples. Let’s begin – How to find Point of Intersection of Two Lines Let the equations of two lines be \(a_1x + b_1y + c_1\) = 0 and, \(a_2x + b_2y + c_2\) = 0 Suppose these two lines intersect at
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Here you will learn method of difference in sequences and series with examples. Let’s begin – Method of Difference Some times the \(n^{th}\) term of a sequence or a series can not be determined by the method, we have discussed earlier. So we compute the difference between the successive terms of given sequence for obtained
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Here you will learn sum of gp to infinity (sum of infinite gp) and its proof with examples. Let’s begin – Sum of GP to Infinity (Sum of Infinite GP) The sum of an infinite GP with first term a and common ratio r(-1 < r < 1 i.e. , | r | < 1)
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