1 Interchanging two rows of a matrix R

1. Interchanging two rows of a matrix R 1 ↔ R 2

2. Multiplying a row of a matrix by a nonzero number (Multiply 3 with Row 2)

3. Adding a multiple of one row of a matrix to a different row of that matrix R 1+R 2 (Leave R 1 unchanged Operation done at R 2)

Ri↔ Rj Interchange rows Ri and Rj. Multiply row Ri by the nonzero constant k. Add k times to row Ri (but leave Rj unchanged), (or add or subtract rows).

A matrix is said to be a reduced matrix provided that all of the following are true 1. All zero-rows are at the bottom of the matrix. 2. For each nonzero-row, the leading entry is 1, and all other entries in the column in which the leading entry appears are zeros. 3. The leading entry in each row is to the right of the leading entry in any row above it.

In problem 1 -6, Determine whether the matrix is reduced or not reduced ? Ex 6. 4. Pg 257

Reduce the given Matrix Q 7, Ex 6. 4. Pg 257 R 1 unchanged 4 R 1 -R 2 Operation at R 2 R 1 unchanged Operation at R 2 Operation at R 1 3 R 2 -R 1 R 2 unchanged Reduced Matrix

Reduce the given Matrix Q 9, Ex 6. 4. Pg 257 R 1 -R 2 R 1 -R 3 Reduced Matrix

Q 7 -12. Reduce the given matrix? YOUR TURN Q 8. Ex 6. 4. Pg 257

Q 13 -26. Solve the system by the method of reduction Q 13 2 x-7 y=50, X+3 y=10 Ex 6. 4. , Pg 257 R 1 ↔ R 2

Reduced Matrix

Q 13 -26. Solve the system by the method of YOUR TURN Q 15. reduction Ex 6. 4. Pg 257