find the rank of 4 1 3 3

kibruyisfa kibruyisfa 2022-06-03 Answered

find the rank of 4 1 3 3 3

                               7 -1 6 0 6

                                2 3 8 2 8

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Answers (1)

Haidar Ali
Answered 2022-07-22 Author has 4 answers

The rank of a matrix is the number of non-zero rows in the echelon form of the matrix. The echelon form can be obtained by row operations such that the leading entry of each row must have zeros below it.

The given matrix is:

                                                     413337-160623828

Divide R3 by 2:

                                                     413337-1606132414

Replace R1 by R1-4R3:

                                                            4-41-4(32)3-4(4)3-4(1)3-4(4)7-1606132414

Rewrite the above matrix:

 

                                                          0-5-13-1-137-1606132414

Interchange  R1 with R3:

                                                         1324147-16060-5-13-1-13

Replace R2 by R2-7R1:

                                                         1324147-7(1)-1-7(32)6-7(4)0-7(1)6-7(4)0-5-13-1-13

Rewrite the above matrix:

                                                      1324140-232-22-7-220-5-13-1-13

Multiply  R2 by -2, we get:

                                                      1324140234414440-5-13-1-13

Replace R3 by R3+523R2:

                                                     1324140234414440-5+523(23)-13+523(44)-1+523(14)-13+523(44)

Rewrite the above matrix:

                                                     13241402344144400-79234723-7923

Multiply  R3 by -23:

 

                                                     1324140234414440079-4779

The above matrix is the echelon form of the given matrix. As the number of non-zero rows in the echelon form of the given matrix is 3, it follows that the rank of the given matrix is 3.

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