MATH SOLVE

3 months ago

Q:
# If the null space of a 4 x 9 matrix is 5-dimensional, what is the dimension of the column space of the matrix? Explain your answer b) (3 points) If A is a 7 x 3 matrix, what is the smallest possible dimension of Nul A? Explain your answer

Accepted Solution

A:

Answer : Dimension of column A is also be 4 whereas the two vector basis lie in R⁴.The smallest possible dimension of Nul A would be zero.Step-by-step explanation:Since we have given that A is matrix of 4 x 9 .so, Number of rows = 4Number of columns = 9Nul A = 5 It means that Rank of A would be 9 - 5 =4So, rank A = 4Thus, dimension of column A is also be 4 whereas the four vector basis lie in R⁴.So, dim Col A = 4If A is 7 x 3 matrix.So, we know that rank A + dim (null A) = 3so, it is possible to have rank A = 3 so the dim col A should be 3Then the smallest possible dimension of Nul A would be zero.