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# 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 1 2 3 4 Row 2 1 3 5 6 Row 3 0 1 2 3 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 1 2 3 4 Row 2 3 9 15 18 Row 3 0 1 2 3
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 1 2 3 4 Row 2 3 9 15 18 Row 3 0 1 2 3 We illustrate this by adding four times Row 1 to Row 3. [1] [2] [3] [4] Row 1 1 2 3 4 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 1 2 3 4 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 1 2 3 4