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Identity or Unit Matrix
A square matrix A=[a i j ] n x n is called an identity or unit matrix if (2) a i j =1 for all i = j In other words a square matrix each of whose diagonal elements is unity and each of whose non-diagonal elements is equal to zero is called an identity or unit matrix. The identity matrix of ..
A square matrix A=[a i j ] n x n is called an identity or unit matrix if (2) a i j =1 for all i = j In other words a square matrix each of whose diagonal elements is unity and each of whose non-diagonal elements is equal to zero is called an identity or unit matrix. The identity matrix of ..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..Suggested answer:
The arrangement is as shown in the figure, the boy X will have B 2 , B 3 as neighbours. The girl Y will have G 2 , G 3 as neighbours. The two boys B 2 , B 3 can be arranged in two ways. The two girls G 2 , G 3 can be arranged in two ways. Hence, the total number of arrangements = 2 x 2 = ..
The arrangement is as shown in the figure, the boy X will have B 2 , B 3 as neighbours. The girl Y will have G 2 , G 3 as neighbours. The two boys B 2 , B 3 can be arranged in two ways. The two girls G 2 , G 3 can be arranged in two ways. Hence, the total number of arrangements = 2 x 2 = ..Theorem:
The number of combinations of n dissimilar things, taken r at a time is..
The number of combinations of n dissimilar things, taken r at a time is..Note:
1. O!= 1 2. When n is a negative or fraction, n! is not defined...
1. O!= 1 2. When n is a negative or fraction, n! is not defined... Result
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