Suppose that B is a 13 times 8 matrix with nullity 6. For each of the following subspaces, tell me
their dimension, along with what value of k is such that the subspace in question is a subspace of
R^k. (For example, a possible - though incorrect - answer is that Col B is a subspace of R^2.) So,
you\'ll need eight answers for this problem (two answers for each of the four parts). Col B Null
B Row B Null B^T
Solution
The nullity of B is 6. Therefore, its rank is 8-6 = 2. Since row rank and column rank of a matrix
are equal, the dimension of Col(B) is 2. Col (B) is a subspace of R8. The nullity of B is 6.
Therefore, the dimension of Null(B) is 6. Null(B) is a subspace of R8. Since the rank of B is 2,
the dimension of Row (B) is 2. Row (B) is a subspace of R13. The dimension of Null(BT) is 13-
rank(B) = 13-2 = 11. Null(BT) is a subspace of R13..
Suppose that B is a 13 times 8 matrix with nullity 6. For each of the.pdf
1. Suppose that B is a 13 times 8 matrix with nullity 6. For each of the following subspaces, tell me
their dimension, along with what value of k is such that the subspace in question is a subspace of
R^k. (For example, a possible - though incorrect - answer is that Col B is a subspace of R^2.) So,
you'll need eight answers for this problem (two answers for each of the four parts). Col B Null
B Row B Null B^T
Solution
The nullity of B is 6. Therefore, its rank is 8-6 = 2. Since row rank and column rank of a matrix
are equal, the dimension of Col(B) is 2. Col (B) is a subspace of R8. The nullity of B is 6.
Therefore, the dimension of Null(B) is 6. Null(B) is a subspace of R8. Since the rank of B is 2,
the dimension of Row (B) is 2. Row (B) is a subspace of R13. The dimension of Null(BT) is 13-
rank(B) = 13-2 = 11. Null(BT) is a subspace of R13.
