Cramer's rule for the solution of a system of equations in 2 variables
We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio..
We recall from our earlier classes that a system of linear equation with two variables is given by This system of linear equation may have either one solution or infinitely many solutions or no solutio..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...Suggested answer:
We have 3A - 2B = 3A+(-2)..
We have 3A - 2B = 3A+(-2)..Example:
The matrices are identify matrices of order 2 and 3 respectivel..
The matrices are identify matrices of order 2 and 3 respectivel..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...Theorem:
The number of permutations of n dissimilar things taken r ..
The number of permutations of n dissimilar things taken r ..General Series
1. To find the sum of first n natural numbers. ..
1. To find the sum of first n natural numbers. ..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.,..Sigma Notation
The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3n. Thu..
The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3n. Thu..See what our Users say :
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