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If A is a 2x2 matrix with eigenvalues 1 and -1, what is the determinant of A?

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Question: If A is a 2x2 matrix with eigenvalues 1 and -1, what is the determinant of A?

Options:

  1. 0
  2. 1
  3. -1
  4. 2

Correct Answer: -1

Solution: 

The determinant of a matrix is the product of its eigenvalues. Thus, det(A) = 1 * (-1) = -1.

If A is a 2x2 matrix with eigenvalues 1 and -1, what is the determinant of A?

Practice Questions

Q1
If A is a 2x2 matrix with eigenvalues 1 and -1, what is the determinant of A?
  1. 0
  2. 1
  3. -1
  4. 2

Questions & Step-by-Step Solutions

If A is a 2x2 matrix with eigenvalues 1 and -1, what is the determinant of A?
  • Step 1: Understand that a 2x2 matrix A has two eigenvalues.
  • Step 2: Identify the given eigenvalues of matrix A, which are 1 and -1.
  • Step 3: Recall that the determinant of a matrix is calculated by multiplying its eigenvalues together.
  • Step 4: Multiply the eigenvalues: 1 * (-1).
  • Step 5: Calculate the result: 1 * (-1) = -1.
  • Step 6: Conclude that the determinant of matrix A is -1.
  • Eigenvalues and Determinants – The determinant of a matrix can be calculated as the product of its eigenvalues.
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