Finding the eigenvalues and eigenvectors of matrix A = 2-1103-12213 Finding matrix A = 2 - 1 0 3 -1 Eigenvalues and eigenvectors of 2 1 3

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• 1. Find the eigenvalues and eigenvectors of the following matrices Find the eigenvalues and eigenvectors of the following matrices 1 6 0 2 2 0 0 0 5
• 2. Let the adjoint matrix of square matrix A of order n be a *, and prove that: (1) if | a | = 0, then | a * | = 0; （2）|A*|=|A|^(n-1) The first question can be asked by the inverse method
• 3. 1. Let a be a nonzero matrix of order n, a * be the adjoint matrix of a, and a * = at. It is proved that | a | ≠ 0
• 4. Let a be a real matrix of order n, and prove that if AA '= 0, then a = 0 How can I prove it? I don't know what matrix a 'is,
• 5. Let a = (1,0,1) t, matrix A = AA, linear algebra Let a = (1,0,1) t, matrix A = AAT, find a ^ n and [2I + a]
• 6. Linear algebra problem: let a be a square matrix of order n, a * be the adjoint matrix of a, if / A / = a ≠ 0, then / A * / = () Let a be a square matrix of order n, and a * be the adjoint matrix of A. if / A / = a ≠ 0, then / A * / = () A、a B、an-1 C、1/a D、an In option B, n-1 is superscript, and in option D, n is superscript!
• 7. Let a be a matrix of order n, n be an odd number, satisfy AA ^ t = e, / A / = 1, find / a-e/
• 8. How to use row elementary row transformation to find invertible matrix, and is there any formula to find the nth power of matrix?
• 9. What is the formula of the sum of cubes? That is, it can calculate the third power of 1 + the third power of 2 + the third power of 3 What's the best one?
• 10. On covariance and covariance matrix formula It is well known that the covariance (x1-e) is not one of the covariance (x1-1)
• 11. Finding the real eigenvalues of a matrix and the corresponding eigenvectors - 3, - 1, 20, - 1, 4 - 1, 0, 1 are matrices -3， -1， 2 ，0 ，-1， 4 ，-1， 0 ，1
• 12. Let a be a matrix of order 3, and | a | = 6. If an eigenvalue of a is 2, then a * must have an eigenvalue of?
• 13. Let n-order matrix be an example of linear algebra A=(1 b .b) (b b .b) b 1 .b b b .b ..........= ..........+(1-b)E b b b 1 b b b b Find the eigenvalue and eigenvector of A
• 14. On matrix in linear algebra~ a 1 1 1 1 a 1 1 Given that the rank of matrix A = 1 is 3, then a =? Why? 1 1 1 a a 1 1 1 1 a 1 1 1 1 a 1 1 a this is matrix A
• 15. What does matrix commutativity mean?
• 16. Do two similar matrices AB have the same rank in linear algebra
• 17. On the problem of matrix in linear algebra Let a ∧ 3 = 2E, prove that a + 2E is invertible, and find (a + 2e) ∧ - 1
• 18. Related problems of matrix in linear algebra~ Let a be a third-order matrix, and AJ be the j-th column of a (J = 1,2,3), Matrix B = (a3,3a2-a3,2a1 + 5A2), (the numbers after a are subscripts) If | a | = - 2, then | B | = (?)
• 19. Let a be a matrix of order n and satisfy that the square of a = e, and prove that R (A-E) + R (a + e) = n
• 20. Let the matrix A = (30; 21) and ab = a + 2B, and then find B, The final answer should be (3, 0; 4) to be more accurate, I just don't know the inverse operation, a-2e = (1, 0; 2 - 1), why the inverse of (a-2e) is (1, 0; 2 - 1), the reciprocal of 2 * 2 matrix, isn't it "sub diagonal elements plus negative sign, main diagonal elements exchange?"?