Vector Worksheets With Answers - Math 125, Exam 3 Page 12
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19This also could have been solved be recalling that the row rank = column rank. Since
the matrix A in reduced row echelon form has row rank 3, we know the dimension of the
column space is 3.
(d) (1 pts) What is the dimension of the null space? Explain your answer.
Solution: Recall that the definition of nullity is the dimension of the null space. By the-
orem, we know the rank + nullity = the number of columns. We have 3 + nullity = 5.
Therefore the nullity is 2.
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