FoundationNumeric answer
A matrix has rank . What is the dimension of its null space?
Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.
The worked solution is in Premium
The answer, the full working and the one idea to take away – for this and all 1,322 questions in the bank. Answer it in practice and your working is marked, with a known mistake named when you make one.
Learn the method
The four fundamental subspaces, and when Ax = b has a solution
Reported in interviews at
More linear algebra questions
- What is the rank of [[1, 2, 3], [4, 5, 6], [7, 8, 9]]?Foundation
- When does Ax = b have at least one solution?Applied
- A is a 3 × 5 matrix of rank 3. How many solutions does Ax = b have for a given b?Applied
- A 3 × 3 matrix has eigenvalues 3, −1 and 2. What is its determinant?Foundation
- Square matrices A and B have det A = 2 and det B = −3.Foundation
- What is the top-left entry of the inverse of [[4, 7], [2, 6]]?Foundation