Inverse of a MatrixDate: 12/29/97 at 20:00:55 From: BMCcheer1 Subject: *please help* Hello, my name is Beth Catanzaro, and I am a 9th grade honors algebra student. I attend Coventry Middle School in Coventry Rhode Island and during vacation, am currently working on an important, but extremely difficult algebra project. This is where I run into a few problems and hope you can help. First off, the teacher has not taught us the material we are working with. He felt it would benefit us more to give out a packet containing all (or most) of the information we would need to answer his written questions. This is where my problems start. My first question as of now would be, "How do you figure out the inverse of a 2 x 2 matrix, such as [5 4] [2 2] ? The question asks to find the determinant, which I already know is ad-bc, but the explanation stops after that, so I don't know what to do next. If you could please help me, I would greatly appreciate it. Beth Date: 12/30/97 at 07:57:49 From: Doctor Jerry Subject: Re: *please help* Hi Beth, I'll assume that you know that in a system of equations you can do three things without changing the set of solutions. 1. multiply any equation by a nonzero constant 2. interchange any two equations 3. add to any equation a multiple of another equation From what you've said, I'll also assume that for the system a*x+b*y = r c*x+d*y = s you know about augmented matrix a b r c d s and that corresponding to 1, 2, and 3 above, there are the three row operations i. multiply any row by a nonzero constant ii. interchange any two rows iii. add to any row a multiple of another row Here's a method for calculating the inverse of the coeffcient matrix: Start with the special augmented matrix a b 1 0 c d 0 1 This is the coefficient matrix to which has been adjoined the identity matrix. Now, do row operations on this matrix, working until you obtain 1 0 A B 0 1 C D The matrix on the right is the inverse of the original coefficient matrix. This method is a very efficient method of calculating the inverse. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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