basic linear algebra elements

The set of first elements in a relation is called Domain. In example (6), Domain is set A = {1, 2, ..

Consider a linear equations in two variables , say, 3x - 2y = 5. It has an infinite number of solutions, some of these are x = 0, Consider a linear equations in two variables , say, 3x - 2y = 5. It has an infinite number of solutions, some of these are x = 0, y = 0. Similarly, if we take ..

Finding the solution by the method of substitution. Finding the solution by the method of substitution. (i) Coefficients of one of the variables (say x) in the two equations are made equal, by multiplying them with suitable factors. (ii) By addition or subtraction, this variable (x) is elimina..

The relation should be one-one or many-one, and Every first element is mapped which means that every pre-image should have an imag..

Let A and B be two non-empty sets.Let A and B be two non-empty sets. A function f from A to B is an association of every element of A to an unique element in B. We write this as f : A g B. A is called the domain. B is called the co-doma..

Functions - Let A and B be two non-empty sets.Let A and B be two non-empty sets. A function f from A to B is an association of every element of A to an unique element in B. We write this as f : A g B. A is called the domain. B is called the co-doma..

Function - Any relation on A x B in which (i) no two second elements have a common first element and (ii) every first element has a corresponding second element is called a function.Any relation on A x B in which (i) no two second elements have a co..

Relation - Consider the following sentences:Consider the following sentences: 42 is a multiple of 6. Line l is parallel to line m. 10 is greater than 7. In each case the first element is related to the last element by the relation in italics. The two elements named are..

There is many-one correspondence between the elements of the set A and the set B..

Every one element of A corresponds to one element of B. Every first element has a corresponding second element. One-one relations in examples 1 and 2 are called one-one functions. Every element of set A has one image in set B. {(1, 4), (2, 4), (3..