tut3 - Solving Systems of Equations: A brief tutorial for...

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1 Solving Systems of Equations: A brief tutorial for 15.053 This is a very brief introduction to solving systems of equations. You probably learned these techniques in high school, and you certainly learned them if you had 18.06 or any other type of linear algebra course. Cleaver, an MIT Beaver It doesn’t hurt to review. And perhaps you’ll learn something new.
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2 Elementary Row Operations The following is a 3 x 4 matrix on which we will perform three types of elementary row operations. [1] [2] [3] [4] Row 1 1234 Row 2 1356 Row 3 0123 The first elementary row operation consists of multiplying one row by a constant. We illustrate this by multiplying Row 2 by 3. [1] [2] [3] [4] Row 1 Row 2 3 9 15 18 Row 3
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3 The Second Elementary Row Operation The second elementary row operation consists of adding a multiple of one row of a matrix to another row of the matrix. [1] [2] [3] [4] Row 1 1234 Row 2 3 9 15 18 Row 3 0123 We illustrate this by adding four times Row 1 to Row 3. [1] [2] [3] [4] Row 1 Row 2 3 9 15 18 Row 3 4 9 14 19
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4 The Third Elementary Row Operation The third elementary row operation consists of interchanging two rows of a matrix. [1] [2] [3] [4] Row 1 1234 Row 2 3 9 15 18 Row 3 4 9 14 19 We illustrate this by interchanging Row 1 and Row 3. [1] [2] [3] [4] Row 1 4 9 14 19 Row 2 3 9 15 18 Row 3
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5 Summary of Elementary Row Operations (EROs) ERO 1: Multiply a Row by a constant ERO 2: Add a multiple of one Row to another ERO 3: Interchange two rows. These operations may be simple, but they are very powerful for solving equations. Cleaver
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6 A Website for Using Elementary Row Operations You can carry out elementary row operations by hand, or using Excel. There is also a site developed by IFORS Tutor for carrying out elementary row operations. Here is the URL http://www.tutor.ms.unimelb.edu.au/frame.html And then click on Row Operations and then go to the ROWOPS Operations Center.
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7 Using the ROWOPS Machine: ERO 1 To Multiply a Row by a constant, put the constant in the operator input box, select the left button for the row, and click on the operator box for row multiplication. Here we multiply Row 2 by 3.
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8 Using the ROWOPS Machine: ERO 2. To add a multiple of one row to another, select the right radio button of the first row, the left radio button of the second row, put the multiplier in the operator input box, and then select the operator for adding a multiple of one row to another.
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This note was uploaded on 01/18/2012 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.

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tut3 - Solving Systems of Equations: A brief tutorial for...

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