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Finite Chapter 2.2 Notes

Finite Chapter 2.2 Notes - *Writing a Type 2 row...

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Math 120 SP08 Section 2.2 Notes Brodnick Using Matrices to Solve Problems Elementary Row Operations : (will not change the solution of a system of equations) *Write the operation next to the row to be changed * 1. Replace a row with a multiple of that row *Note: if you want to divide, multiply by a fraction 2. Replace a row by multiplying it by a number (not 0) and adding or subtracting a multiple of another row 3. Switching the order of the rows Steps to solving a system using row operations : (a.k.a. Row Reduction or Gauss-Jordan Reduction ) *Goal : make the matrix look like # 1 0 # 0 1 (ones on main diagonal, zeros above and below) 1. Write coefficient rows into one set of brackets ( Augmented Matrix ) 2. Clear any fractions with a Type 1 row operation 3. The first nonzero entry in Row 1 (R1) is the Pivot (pivots will be used to clear a column) 4. Use the pivot to clear its column (make entries above and below the pivot zeros) with a Type 2 row operation
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Unformatted text preview: *Writing a Type 2 row operation (for a 2-equation system): a. Write the row to be changed first, and the row containing the pivot second b. Mismatch: multiply R2 by the absolute value of the pivot in R1, and multiply R1 by the absolute value of the entry below the pivot in R2 c. If the entries in the pivot column have opposite signs , add ; if they have the s ame sign , s ubtract 5. Simplify – if at any time a row can be reduced, do it 6. In R2, the first nonzero entry is the new pivot – clear the new pivot column 7. Change each pivot to a 1 with a Type 1 row operation, and rewrite the matrix as a system of equations Matrices on the calculator : 2 nd 1-x or MATRIX → → EDIT # of rows × # of columns type in entries, pressing ENTER after each 2 nd MODE 2 nd 1-x or MATRIX → MATH B: rref( 2 nd 1-x or MATRIX choose the matrix you entered from the names list ENTER...
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