Which statement best describes a non-singular matrix?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $9.99Unlock all

Boost your skills in A Level Further Mathematics Core Pure. Study with flashcards and multiple choice questions, each question is followed by hints and explanations. Get prepared for your exam with confidence!

Multiple Choice

Which statement best describes a non-singular matrix?

Explanation:
Non-singular means you can reverse what the matrix does. For a square matrix, that means there exists another matrix that undoes it, giving the identity—this is the inverse. Equivalently, a non-singular matrix has a nonzero determinant and its columns are linearly independent. So the statement that best describes it is that it has an inverse. If the determinant were zero, it would be singular and not invertible. Being non-square (more rows than columns) or being symmetric doesn’t determine invertibility on its own.

Non-singular means you can reverse what the matrix does. For a square matrix, that means there exists another matrix that undoes it, giving the identity—this is the inverse. Equivalently, a non-singular matrix has a nonzero determinant and its columns are linearly independent. So the statement that best describes it is that it has an inverse. If the determinant were zero, it would be singular and not invertible. Being non-square (more rows than columns) or being symmetric doesn’t determine invertibility on its own.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy