Eigenvalues And Eigenvectors Mock Tests

The eigenvalues of the matrix [[2, 1], [1, 2]] are

Let A be a 2 × 2 matrix with det(A) = 2 and tr(A) = 3. The determinant of A² − 3A + 2I is

The eigenvalues of a skew-symmetric matrix are

Let T: ℝⁿ → ℝⁿ be a linear transformation such that T² = T. If det(T + I) ≠ 0, then T is

Let A be a 3 × 3 matrix with eigenvalues 1, 2, and 3. The trace of A³ is

Let A be a 3 × 3 matrix with eigenvalues 1, 2, and 3. The determinant of (A³ − 6A² + 11A − 6I) is

The minimum number of linearly independent eigenvectors of a 3 × 3 matrix with characteristic polynomial (λ − 1)²(λ − 2) is

Let A be a 3 × 3 matrix with eigenvalues 1, 2, and 3. The determinant of A³ is