Question

Find the bases for Col A and Nul​ A, and then state the dimension of these subspaces for the matrix A and an echelon form of A below.

A= 1    3    8 2     7               1 3 8 2 7

      2    7    20    6     20    ---       0 1 4 2 6

      -3   -12   -36    -7   -19             0 0 0 1 4

       3    13 40    9     25             0 0 0 0 0

Start 4 By 5 Table 1st Row 1st Column 1 2nd Column 3 3rd Column 8 4st Column 2 5st Column 7 2nd Row 1st Column 2 2nd Column 7 3rd Column 20 4st Column 6 5st Column 20 3rd Row 1st Column negative 3 2nd Column negative 12 3rd Column negative 36 4st Column negative 7 5st Column negative 19 4st Row 1st Column 3 2nd Column 13 3rd Column 40 4st Column 9 5st Column 25 EndTable

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Start 4 By 5 Table 1st Row 1st Column 1 2nd Column 3 3rd Column 8 4st Column 2 5st Column 7 2nd Row 1st Column 0 2nd Column 1 3rd Column 4 4st Column 2 5st Column 6 3rd Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 1 5st Column 4 4st Row 1st Column 0 2nd Column 0 3rd Column 0 4st Column 0 5st Column 0 EndTable

A basis for Col A is given by

StartSet nothing EndSet

.

​(Use a comma to separate vectors as​ needed.)

The dimension of Col A is

3

.

A basis for Nul A is given by

StartSet nothing EndSet

.

​(Use a comma to separate vectors as​ needed.)

The dimension of Nul A is

.

Answer 1

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