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Essay on Importance of Linear algebra in Engineering Design Methodology
Most mathematicians define Linear Algebra as that branch of mathematics that deals with the study of vectors, vector spaces and linear equations. Modern mathematics also relies upon linear transformations and systems of vector matrix. Analytic geometry utilizes the techniques learned during a study of linear algebra, for analytically computing complex geometrical shapes. In addition to science, engineering and mathematics, linear algebra has extensive applications in the natural as well as the social sciences. Linear algebra today has been extended to consider n-dimensional space. Although it is very difficult to visualize vectors in n-space, such n-dimensional vectors are extremely useful in representing data. One can easily summarize and manipulate data efficiently in this framework, when data are ordered as a list of n components.
Since the students who take pre-calculus have very little knowledge about the subject of matrices, it has become very important to treat the subject matter in depth. In 1989, the NCTM recognized the need for greater emphasis on linear algebra and stated that "matrices and their applications" should receive "increased attention" in high school curriculum. It should be recognized that linear algebra is as important as calculus to scientists and engineers
In linear algebra one studies sets of linear equations and their transformation properties. It is possible to consider the analysis of rotations in space, selected curve fitting techniques, differential equation solutions, as well as many other problems in science and engineering using techniques of linear algebra. Two tools are extensively used in linear algebra. They are: The Matrix and The Determinant. Solution to a vector matrix model equation is regarded as one of the most important of ‘central problems’ of linear algebra.
Study of vectors in two dimensional as well as three dimensional space is extremely important for design engineers..........
