Why is the basis of the null space of matrix B in R4?

Is the number of components in each vector in matrix B in the null space calculated using the number of variables in matrix B (in this case 4)?

Then the row/column space is in R3 as there are 3 pivot rows/columns?

Question

Why is the basis of the null space of matrix B in R4?

Is the number of components in each vector in matrix B in the null space calculated using the number of variables in matrix B (in this case 4)?

Then the row/column space is in R3 as there are 3 pivot rows/columns?

holsteremission · Answer

What is $\mathbf B$?

subbie · Answer

Somehow my image is appearing on the app but not on the site.

B= [1 1 0       [ 1 0 -1 2
      0 1 0         0 1 1 -1
      1 0 1 ]       0 0 0 0]

holsteremission · Answer

It's not entirely clear what it is... Can you try using the draw tool maybe?

subbie · Answer

Hi Holster, here you go

|dw:1480840553480:dw|