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Determinants: 2×2 Determinants (page 1 of 2) Sections: 2×2 determinants, 3×3 determinants Determinants are like matrices, but done up in absolutevalue bars instead of square brackets. There is a lot that you can do with (and learn from) determinants, but you'll need to wait for an advanced course to learn about them. In this lesson, I'll just show you how to compute 2×2 and 3×3 determinants. (It is possible to compute larger determinants, but the process is much more complicated.) If you have a square matrix, its determinant is written by taking the same grid of numbers and putting them inside absolutevalue bars instead of square brackets:
Just as absolute values can be evaluated and simplified to get a single number, so can determinants. The process for evaluating determinants is pretty messy, so let's start simple, with the 2×2 case. For a 2×2 matrix, its determinant is found by subtracting the products of its diagonals, which is a fancy way of saying in words what the following says in pictures:
In other words, to take the determinant of a 2×2 matrix, you multiply the toplefttobottomright diagonal, and from this you subtract the product of bottomlefttotopright diagonal. "But wait!" I hear you cry; "Aren't absolute values always supposed to be positive? You show that second matrix above as having a negative determinant. What's up with that?" You make a good point. Determinants are similar to absolute values, and use the same notation, but they are not identical, and one of the differences is that determinants can indeed be negative.
I multiply the diagonals, and subtract: Copyright © Elizabeth Stapel 20042011 All Rights Reserved
I convert from a matrix to a determinant, multiply along the diagonals, subtract, and simplify: Top  1  2  Return to Index Next >>



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