Matrix_1 - Matrices Objectives: At the end of this lesson,...

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Matrices 1 Gaussian Elimination is also called Gauss-Jordan Reduction . Either term refers to using the standard row operations to find the rref form of the matrix. © Arizona State University, Department of Mathematics and Statistics 1 of 3 Objectives: At the end of this lesson, you should be able to: 1. Create a matrix from a linear system 2. Identify the various kinds of matrices we can create from them. 3. Define Gaussian Elimination within matrices 4. Apply Gaussian Elimination to a matrix. Background Remember synthetic division? It made polynomial division simpler by relying only on the position of the various degrees of the variable. It’s not an uncommon practice in math to let position dictate size, degree or otherwise relate to a number such as a coefficient. We do it with numbers all the time. That’s how we know that 10001 is a lot more than 101. We do exactly the same thing with linear systems. Think back to all of our Gaussian Conventions. We always said we would add or otherwise combine the columns of like variables. If we just drop out the variables, we create an array of coefficients or constants. As long as we don’t jumble the order on any row, position alone should allow us to do the various row operations. You may have already done this in the set-up for linear optimization. However, it won’t hurt to review the process. Gaussian 1 Elimination in Matrices Take a look at this system: 1 1 2 3 2 1 2 3 3 1 2 3 : 3 3 5 : 2 4 2 1 : 4 5 2 2 r x x x r x x x r x x x - + = - + = - + = Rectangular arrangements of numbers are called matrices. ( Matrix is the singular). We can create a number of arrays from this system. Suppose we decide to just look at the coefficients. The system
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Matrix_1 - Matrices Objectives: At the end of this lesson,...

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