If a 2x2 matrix has determinant zero, what can be said about the 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

Prepare for the A Level Further Mathematics Core Pure Test with detailed explanations and challenging questions. Boost your understanding and confidence to excel in your exam!

Multiple Choice

If a 2x2 matrix has determinant zero, what can be said about the matrix?

Explanation:
When a 2x2 matrix has determinant zero, the transformation it represents collapses area to zero, so it is singular. This means the two columns (or rows) are linearly dependent, the matrix doesn’t have full rank, and it cannot be inverted. In other words, there is no unique inverse matrix. Because the determinant is zero, it cannot be 1, and it is not negative. So the only true description here is that the matrix is singular.

When a 2x2 matrix has determinant zero, the transformation it represents collapses area to zero, so it is singular. This means the two columns (or rows) are linearly dependent, the matrix doesn’t have full rank, and it cannot be inverted. In other words, there is no unique inverse matrix.

Because the determinant is zero, it cannot be 1, and it is not negative. So the only true description here is that the matrix is singular.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy