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Operations on Matrices
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 = ..
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 = ..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 ..
Difference between a Permutation and a Combination
i. In a combination, only selection is made. In a permutation, not only a selection is made, but also there is an arrangement of a definite order. ii. There is no order of selection in combinations. In permutation, order is a must. iii. Usually (i.e., except in specia..
Matrix Addition is commutative
This means that A + B = B + A, where A, B are 2 matrices of the same order..
Note:
If two matrices A and B are not of same order, A + B and A - B are not define..
Introduction
A set of numbers arranged in a definite order according to some definite rule is called a sequenc..
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..
Sequences and Series
Introduction - A set of numbers arranged in a definite order according to some definite rule is called a sequenc..
Example:
The matrices are scalar matrices of order 2 and 3 respectivel..
The matrices are scalar matrices of order 2 and 3 respectivel..Theorem
If A and B are two invertible matrices of the same order, then (AB) - 1 = B - 1 A - 1..
Result
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