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If A is a 2x2 matrix with eigenvalues 1 and -1, what is the determinant of A?
If A is a 2x2 matrix with eigenvalues 1 and -1, what is the determinant of A?
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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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The determinant of a matrix is the product of its eigenvalues. Thus, det(A) = 1 * (-1) = -1.
Questions & Step-by-step Solutions
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Q: If A is a 2x2 matrix with eigenvalues 1 and -1, what is the determinant of A?
Solution:
The determinant of a matrix is the product of its eigenvalues. Thus, det(A) = 1 * (-1) = -1.
Steps: 6
Show Steps
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.
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