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 = ..Examples:
skew-symmetric for every square matrix A. That is any square matrix is expressible as the sum of a symmetric matrix and a skew-symmetric matrix. 5. A matrix which is both symmetric and skew symmetric is a zero matr..
skew-symmetric for every square matrix A. That is any square matrix is expressible as the sum of a symmetric matrix and a skew-symmetric matrix. 5. A matrix which is both symmetric and skew symmetric is a zero matr..Suggested answer:
Find the product (ac), of the coefficient of x 2 and the last term. List the factor pairs of ac. Choose a factor pair whose sum is the coefficient of the middle term. Rewrite the polynomial by splitting the middle term. Regroup and factorise..
Find the product (ac), of the coefficient of x 2 and the last term. List the factor pairs of ac. Choose a factor pair whose sum is the coefficient of the middle term. Rewrite the polynomial by splitting the middle term. Regroup and factorise..Summary
A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if P(n) is ..
Note:
The middle terms may be easily found out by using the following method: i) When n is even, we add the even number 2 to n and divide by 2 to get the middle term i.e., term. ii) When n is odd, we add the odd numbers 1 and 3 to n and divide by 2 to get the middle terms..
The middle terms may be easily found out by using the following method: i) When n is even, we add the even number 2 to n and divide by 2 to get the middle term i.e., term. ii) When n is odd, we add the odd numbers 1 and 3 to n and divide by 2 to get the middle terms..Statement
Some sentences depend on a variable for its truth value (i.e., true or false). e.g., "2+4+6+2n=2n" is true for n=1 but false for n=2, n=3 etc. As the above sentence is definitely true or definitely false for a particular positive integral value of n, the senten..
Example:
E = {x : x 2 = 9 and 3x = 6} is an empty set because there is no number that can satisfy both x 2 = 9 and 3x = 6..
E = {x : x 2 = 9 and 3x = 6} is an empty set because there is no number that can satisfy both x 2 = 9 and 3x = 6..Non-singular Matrix
A square matrix A is said to be non-singular if its determinant value is non-zero. i.e.,..
A square matrix A is said to be non-singular if its determinant value is non-zero. i.e.,..Example 6:
Find a) reciprocal ratio of 3:5 b) duplicate ratio of 2:3 c) triplicate ratio of 3:4 d) sub duplicate ratio of 25:16 e) sub triplicate ratio of 2..
Summary
(i) Let X be a set of numbers and f : N n X be a function, then the ordered set {f(1), f(2),...., f(n)} is called a finite sequence in X. (ii) Let X be a set of numbers and f : N X be a function, then the ordered set {f(1), f(2),....} is called an infi..
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