Providian Fund

In: Business and Management

Submitted By insomniac313
Words 1160
Pages 5
OK, Determinants are Easy, but

What are they good for?

Oops, sorry English Folks, I meant “For what are they good?”

Sometimes it may seem to students that the only value of the thing they have just learned in math is to be able to learn the next thing and although I am a big proponent of the “Math for Math’s sake” school, I occasionally feel a swelling up of my old Engineering background urging me to provide an application of the learning. In just such a mood, I offer the following

APPLICATIONS OF DETERMINANTS

We begin by asking you to recall that moment not so long ago when you were in an algebra or geometry class, and a problem might begin when we gave you the coordinates of three points in the coordinate plane, A=(2,1); B=(5,6) and C= (9,-1). Among the myriad things we might have asked you to do with this given information would be two that are easily answered by the methods of determinants; “Find the area of the triangle formed?” and “Prove that the three points are, or are not, collinear (lie on the same line).”

Finding the area of a triangle If you had not had the benefit of an introduction to determinants, you might have to resort to something like the following to find area. Taking the points in pairs we could find the length of each segment, ([pic], [pic], and [pic]) and then employing the well known formula of Heron (you do remember Heron’s Formula, don’t you?) to find the area. We would arrive at an area of 20.5 square units. But now that you know how to evaluate the determinant of a matrix, we can instead just enter the x values of each point as one column of the matrix, enter the y values as a second column, and add a third column of all ones (someday I will explain about cross products of vectors and this third column will seem more clear). We get the matrix shown at right. And if we evaluate the determinant of the…...

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