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Unformatted text preview: means interchanging i th and j th rows. 2. A row is multiplied by a nonzero constant: R i → kR i means multiplying i th row by a nonzero constant k . 3. A constant multiple of one row is added to another row: R i → R i + kR j means adding i th row by k multiple of j th row. Notice that the above operations are called the row operations . Target: Reduced the augmented matrix to the forms (A) ² 1 0 ³ ³ m 0 1 ³ ³ n ´ , (B) ² 1 m ³ ³ n ³ ³ ´ and (C) ² 1 m ³ ³ n ³ ³ p ´ . Conclusion: 1. We have a unique solution for our system if it reduces to Form A. 2. We have inﬁnitely many solutions if it reduces to Form B. 3. We have no solution if it reduces to Form C. 2 Example 3. Solve the following systems of linear equations: (a) ± 2 x 1x 2 = 46 x 1 + 3 x 2 =12 (b) ± 2 x 1 + 6 x 2 =3 x 1 + 3 x 2 = 2 3...
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 Fall '09
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 Math, Linear Equations, Equations, Multiplication, Matrices, augmented matrix, Howard Staunton

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