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What is a linear transformation?
linear transformation can be define as the vector of 1 function present in other vector are known as linear transformation.
What is an affine transformation?
An affine transformation is a linear transformation between vector spaces, followed by a translation.
How are linear inequalities different from linear equations?
A linear equation represents a line. A linear inequality represents part of the space on one side (or the other) of the line defined by the corresponding equation.
What are the applications of linear transformation in engineering?
There are four forms of linear transformation on the Cartesian plane which is used in engineering and they are:- Translation moves a shape in the same direction and distance Refection is a 'mirror image' of a shape Enlargement changes the size of a shape by a scale factor Rotation turns a shape through an angle at a fixed point
What is linear algebra used for?
Linear algebra is used to analyze systems of linear equations. Oftentimes, these systems of linear equations are very large, making up many, many equations and are many dimensions large. While students should never have to expect with anything larger than 5 dimensions (R5 space), in real life, you might be dealing with problems which have 20 dimensions to them (such as in economics, where there are many variables). Linear algebra answers many questions. Some of these questions are: How many free variables do I have in a system of equations? What are the solutions to a system of equations? If there are an infinite number of solutions, how many dimensions do the solutions span? What is the kernel space or null space of a system of equations (under what conditions can a non-trivial solution to the system be zero?) Linear algebra is also immensely valuable when continuing into more advanced math topics, as you reuse many of the basic principals, such as subspaces, basis, eigenvalues and not to mention a greatly increased ability to understand a system of equations.
