Let the three eigenvalues of a matrix of order 3 be 2, - 4,3, then the three eigenvalues of a * are () A 2,-4,3 B 1/2,-1/4,1/3 C -12,6,-8 D 12,-6,8

RELATED INFORMATIONS

• 1. Let 2 be an eigenvalue of a square matrix of order 3, then a ^ 2 must have an eigenvalue?
• 2. Let the three eigenvalues of a matrix of order 3 be - 1,2,4, then what are the three eigenvalues of a *?
• 3. 4. Let the four eigenvalues of a square matrix of order 4 be 3,1,1,2, then | a|=
• 4. Let a be a square matrix of order n and satisfy a ^ 2-3a + 2E = 0, it is proved that the eigenvalue of a can only be 1 or 2
• 5. If a is a square matrix of order n and AAT = e, | a | = - 1, it is proved that | a + I | = 0, where I is the identity matrix
• 6. If a is a square matrix of order n and AAT = e, | a | = - 1, it is proved that | a + e | = 0, where e is the identity matrix
• 7. Let a square matrix of order n satisfy a ^ 2-3a + 3E = 0, prove that a-2e is invertible, and find its inverse matrix?
• 8. There are four numbers in the equal ratio sequence. Subtract 1,1,4,13 from these four numbers respectively, and then they will become the equal difference sequence again. Find these four numbers
• 9. In the isosceles triangle ABC, ab = AC = 12cm, De is the vertical bisector of the waist AB, de intersects AB to D, BC to e, and BC = 20cm
• 10. Let a square matrix of order n satisfy the square of a - 5A + 7e = 0, prove that 3e-a is invertible, and find the inverse matrix of (3a-e)
• 11. Let a be a square matrix of third order, and it is known that a has two eigenvalues - 1. - 2, and the rank of (a + 3e) is 2. Find the determinant of a + 4E
• 12. Let a be a square matrix of order n, 2,4,..., 2n be the n eigenvalues of a, and calculate the value of determinant / a-3e /
• 13. The eigenvalues of adjoint matrix A * are 1,2,4,8. Find the eigenvalues of (1 / 3a) ^ - 1
• 14. Let a matrix of order 4 satisfy | 3e-a |, AAT = 2E, | a|
• 15. A is a matrix of order n. It is proved that tr (a ^ k) = the sum of the k-th power of the eigenvalues of A
• 16. If the eigenvalue of matrix A is t, why is the eigenvalue of K power of a K power of T,
• 17. Let a matrix of order n have n eigenvalues 0,1,2,..., n-1, and B ~ A, and find det (I + b)
• 18. Given that the matrix A of order n satisfies a ^ 2-2a-3e = 0, it is proved that the eigenvalue of a can only be - 1 or 3. How to prove that it can only be - 1? (- e-A) (3e-a) = 0, but how can we prove that it can only be - 1 or 3?
• 19. Let a be a matrix of order n, | a | ≠ 0, a * be the adjoint matrix of a, and E be the unit matrix of order n. if a has an eigenvalue λ, then (a *) 2 + e must have an eigenvalue______ ．
• 20. If the 3-dimensional column vectors α and β satisfy α 'β = 2, how to find the nonzero eigenvalues of the matrix β α'?