calc 4 Determine the dimensions of NulA and CnlA for the fol

calc 4

Determine the dimensions of NulA and CnlA for the following matrix. [1 0 0 0 3 0 0 0 -4 1 0 0 2 -3 1 0 -1 7 4 0 6 0 -3 0]

Solution

It is a 4x6 matrix

HEnce by rank nullity theorem

dim Nul A+ dim Col A=6

The matrix has three non zero rows with pivots in different columsn so the first three columns are linearly indepdendent and last column is identically 0

Hence, dim Col A=3

So, dim Nul A=3