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Theorem:
The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative] = IC = C i.e., B = C Hence t..
The inverse of a square matrix if it exists, is unique. Let A be an invertible square matrix. If possible, let B and C be two inverse of A. Then AB = BA = I. AC = CA = I (by def. of inverse) Now, B = BI = B(AC) = (BA)C [ Matrix multiplication is associative] = IC = C i.e., B = C Hence t..Examples:
1. Find the sum to the series 1+2x+3x 2 +.... to n terms and to infinity when x < ..
Row Matrix
A matrix having only one row is called a row-matrix. For example: A[1 3 2 -2] is a row matrix of order 1 x..
Example:
are all zero matrices of orders 1 x 2, 2 x 1, 2 x 2 and 3 x 3 respectivel..
are all zero matrices of orders 1 x 2, 2 x 1, 2 x 2 and 3 x 3 respectivel..Examples:
From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..
From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..Suggested answer:
We have 3A - 2B = 3A+(-2)..
We have 3A - 2B = 3A+(-2)..Permutations and Combinations Introduction
Summary - The fundamental principle of counting (F.P.C) states that if an operation can be performed in m different ways and if for each such choice, another operation can be performed in n different ways, then both operations, in succession can be performed in exactly mn different ways. The princi..
Properties of adjoint of a matrix
1. A.(adj A) = (adj A). A = |A| I 2. adj (AB) = (adj B) . (adj ..
Suggested answer:
The given equations are 2x - y + z = -3 3x - 0.y - z = - 8 2x + 6y + 0.z= 2 = 2(6) +1(2) + 1(18) = 12 +2 + 18 = 32 The system has a unique solutions. A 1 1 = (0 + 6) = 6, A 1 2 = -(0 + 2) = -..
The given equations are 2x - y + z = -3 3x - 0.y - z = - 8 2x + 6y + 0.z= 2 = 2(6) +1(2) + 1(18) = 12 +2 + 18 = 32 The system has a unique solutions. A 1 1 = (0 + 6) = 6, A 1 2 = -(0 + 2) = -..Square Matrix
A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n. In this square matrix of order n the elements a 1 1 , a 2 2 .......a n n is called the principal diagonal or the leading diagonal. The elements a 1 1 , a 2..
A matrix in which the number of rows is equal to the number of columns, say n, is called a square matrix of order n. In this square matrix of order n the elements a 1 1 , a 2 2 .......a n n is called the principal diagonal or the leading diagonal. The elements a 1 1 , a 2..See what our Users say :
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