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Operations for

Operations for. Reduced Matrix. 1. Interchanging two rows of a matrix R1 ↔ R2. E lementary Row Operations. 2. Multiplying a row of a matrix by a nonzero number (Multiply3 with Row2). E lementary Row Operations.

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Operations for

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  1. Operations for Reduced Matrix

  2. 1. Interchanging two rows of a matrix R1 ↔ R2 E lementary Row Operations

  3. 2. Multiplying a row of a matrix by a nonzero number (Multiply3 with Row2) E lementary Row Operations

  4. 3. Adding a multiple of one row of a matrix to a different row of that matrix R1+R2 (Leave R1 unchanged Operation done at R2) E lementary Row Operations

  5. 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). E lementary Row Operations Notation Corresponding Row Operation

  6. 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. Reduced Matrix

  7. In problem 1-6, Determine whether the matrix is reduced or not reduced ? Ex6.4. Pg257

  8. Reduce the given Matrix Q7, Ex6.4. Pg257 R1 unchanged 4R1-R2 Operation at R2 R1 unchanged Operation at R2 Operation at R1 3R2-R1 R2 unchanged Reduced Matrix

  9. Reduce the given Matrix Q9, Ex6.4. Pg257 R1-R2 R1-R3 Reduced Matrix

  10. Q7-12. Reduce the given matrix? Ex6.4. Pg257 YOUR TURN Q 8.

  11. Q13-26. Solve the system by the method of reduction Q13 2x-7y=50, X+3y=10 Ex6.4., Pg257 R1 ↔ R2

  12. Reduced Matrix

  13. Q13-26. Solve the system by the method of reduction Ex6.4. Pg257 YOUR TURN Q 15.

  14. THANK YOU

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