Lesson 10.2 – Row Operations and Solving Systems x 3y 5z 8 2x 5y 4z 8 3x 5y 4z 5 2. Write an augmented matrix from the system above and follow the row operations indicated. R2 2r1 r2 R3 3r1 r3 R3 4r2 r3 The resulting matrix is what we call Row Echelon Form and has the general form 1 a b c 0 1 d 0 0 1 1 R3 r3 13 e f 3. Write a system of equations form the resulting augmented matrix from problem 2 and solve. 4. Write the augmented matrix from the following system and convert to row echelon form by the steps indicated. x 3y 4z 4 2x 5y 6z 7 matrix 3x 3y 4z 18 system 1 R3 r3 4 5. Solve the resulting system from problem 4. R2 2r1 r2 R3 3r1 r3 R3 6r2 r3 6. Write the augmented matrix from the following system. Then convert to row echelon form by the steps indicated. 2 x 3 y z 2 matrix x yz 8 3x 2 y 9 z 9 R2 R3 R1 r3 r1 R2 12r3 r2 R3 5r2 r3 R2 2r1 r2 R3 3r1 r3 1 R3 57 r3 R1 r2 r1 R1 R2 The resulting matrix is what we call Row Reduced Echelon Form and has the general form. 1 0 0 a 0 1 0 b 0 0 1 c This form is nice because you can clearly see the solution of the initial system: x = _________ , y = _________, and z = _________. 7. Write the augmented matrix from the following system and convert to row reduced echelon form by the steps indicated. x 3y z 6 2x 5y z 2 matrix x y 2z 7 1 R3 r3 3 R2 2r1 r2 R3 r1 r3 R1 r 3 r1 R 3r r 3 2 2 R3 2r2 r3 R1 3r2 r1 Tips For Writing in Row Reduced Echelon Form x y z 1) Make the number in thefirst row first column (top left) a 1 by switching rows or multiplying it by a nonzero multiple 2) Use this 1 (and row operations) to make everything beneath it a zero 3) Repeat steps 1 and 2 with second row second column number, etc to get in row echelon form 4) Use the 1 in the last row (and row operations) to make everything above it zero 5) Repeat step 4 as you work back up. Step 1 Step 2 Step 5 a 1 1 b 1 c Step 3 Step 4 Note: This example is with three equations with three variables. We will not always work with these. We may have more or less.