GATE EE 2018 Set 1 — Question 27
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Engineering Mathematics → Linear Algebra → Determinants
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Question
Consider a non-singular square matrix A. If and , the determinant of the matrix A is _________(up to 1 decimal place).
Correct answer
5.5 to 5.5
Solution
Let and be the eigenvalues of the matrix .
1.The trace of a matrix is the sum of its eigenvalues:
2.The eigenvalues of are and . The trace of is the sum of these eigenvalues:
3.We use the algebraic identity:
4.Substitute the known values:
5.The determinant of a matrix is the product of its eigenvalues:
Therefore, the determinant of the matrix is 5.5.Continue learning with Success Tracker
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