5 Questions
What is the maximum number of linearly independent vectors in a set of vectors in ℝⁿ?
n
If A is an n × n matrix, then which of the following is true?
A is invertible if and only if its determinant is non-zero
Let A be an n × n matrix. The Cayley-Hamilton theorem states that:
A satisfies its characteristic equation
Let A be an m × n matrix and let T: ℝⁿ → ℝᵐ be the linear transformation defined by T(x) = Ax. What is the rank of A?
the dimension of the image of T
What is the relation between the rank and nullity of a matrix A?
rank(A) + nullity(A) = number of columns of A
Test your understanding of linear algebra concepts, including matrix rank, eigenvalues, eigenvectors, and the Cayley-Hamilton theorem.
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
