Introduction
Lets say there are 6 frogs and 2 crabs in a pond. We can compare the number of frogs to the number of crabs in two different ways: How many more frogs than crabs are there? or How many fewer crabs than frogs are there? The answer to both the questions is same i.e. 6-2=4. There a..
Lets say there are 6 frogs and 2 crabs in a pond. We can compare the number of frogs to the number of crabs in two different ways: How many more frogs than crabs are there? or How many fewer crabs than frogs are there? The answer to both the questions is same i.e. 6-2=4. There a..Arithmetic Geometric Series
A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put we get GP and if we put r = 1, we get an AP. To find the sum to the series Subtracting (ii) from (i), we g..
A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put we get GP and if we put r = 1, we get an AP. To find the sum to the series Subtracting (ii) from (i), we g..Consistency of a system of linear equation
If a system of linear equations has at least one solution, then the system is called consistent, otherwise it is called inconsistent. Solve the system of linear equations (1) by using method of elimination as studied earlier Multiplying the first equation by a 2 and the second..
If a system of linear equations has at least one solution, then the system is called consistent, otherwise it is called inconsistent. Solve the system of linear equations (1) by using method of elimination as studied earlier Multiplying the first equation by a 2 and the second..Some important results
Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then ad = bc This property is..
Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then ad = bc This property is..Matrices and Determinants
Summary - A matrix is defined as a rectangular array of elements. If the arrangement has m rows and n columns, then the matrix is of order mxn (read as m by n). A matrix is enclosed by a pair of parameters such as ( ) or [ ]. It is denoted by a capital letter. Two matrices are said to be comparable..
Subtraction of Matrices
Subtraction of Matrices - Two matrices can be subtracted in the same way as they are added. We change the signs of the corresponding elements and then add them. If then If and , th..
Subtraction of Matrices - Two matrices can be subtracted in the same way as they are added. We change the signs of the corresponding elements and then add them. If then If and , th..Subtraction of Matrices
For two matrices A and B of the same order, we define A-B = A+(-B..
Some properties of Addition and Subtraction of Matrices
(1) A + B = B + A (Commutative property) (2) k(A + B) = kA + kB (Distributive property) (3) (A + B) + C = A + B + C (Distributive property) (4) (A + B) + C = A + (B + C) (Associative property) A + O = O + A = A where O is zero or null matrix. A = A + O (5) A + (-A) = O (-A is additive inverse of A)..
(1) A + B = B + A (Commutative property) (2) k(A + B) = kA + kB (Distributive property) (3) (A + B) + C = A + B + C (Distributive property) (4) (A + B) + C = A + (B + C) (Associative property) A + O = O + A = A where O is zero or null matrix. A = A + O (5) A + (-A) = O (-A is additive inverse of A)..Properties of Polynomials
Addition and subtraction of two polynomials mean combining like terms. We can perform multiplication and division al..
Simplification of fractions
Remember 'BODMAS', Do the various operations in the order given below: Open brackets from within and go outwards in the order: -, (), {} and lastly []. B 1 Brackets O 2 Of D 3 Division M 4 Multiplication A 5 Addition S 6 Subtraction..
Result
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