Section 1.1: Systems of Linear Equations A linear equation: a1x1 ...

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Matrix Notationx 1 2x 2 1x 1 3x 2 31 21 3(coefficient matrix)x 1 2x 2 1x 1 3x 2 31 2 11 3 3(augmented matrix)x 1 2x 2 1x 2 21 2 10 1 2x 1 3x 2 21 0 30 1 26
Elementary Row Operations:1. (Replacement) Add one row to a multiple of another row.2. (Interchange) Interchange two rows.3. (Scaling) Multiply all entries in a row by a nonzero constant.Row equivalent matrices: Two matrices where one matrix canbe transformed into the other matrix by a sequence of elementaryrow operations.Fact about Row Equivalence: If the augmented matrices of twolinear systems are row equivalent, then the two systems have thesame solution set.7
Page 1 and 2: Section 1.1: Systems of Linear Equa
Page 3 and 4: EXAMPLE: Three equations in three v
Page 5: x 2 x 2−10 −5 5 10 x 14422−10
Page 9 and 10: x 1 29x 2 16x 3 31 0 0 290 1 0 1
Page 11 and 12: EXAMPLE: Is this system consistent?

Section 1.1: Systems of Linear Equations A linear equation: a1x1 ...

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