Solution:

                                            ̃            ̃             ̃           ̃            ̃

                      (     )           (           )        (             )       (            )   (       )




                                        [                          ][          ]   [ ]




[                     | ]           [                            | ]                [                   |           ]




[                     |         ]           [                              |            ]




[                 |         ]                                          |
                                                [                                           ]

The system is consistent.                           can be any values. Therefore the vector span                .
Solution:




[               | ]             [                 | ]             [       | ]




[                     | ]           [                       | ]       [         | ]




            [                           | ]             [                 | ]




                            (       )(        )

Tutorial 2, 2(e), no. 7

  • 1.
    Solution: ̃ ̃ ̃ ̃ ̃ ( ) ( ) ( ) ( ) ( ) [ ][ ] [ ] [ | ] [ | ] [ | ] [ | ] [ | ] [ | ] | [ ] The system is consistent. can be any values. Therefore the vector span .
  • 2.
    Solution: [ | ] [ | ] [ | ] [ | ] [ | ] [ | ] [ | ] [ | ] ( )( )