Let the eigenvalues of the third order invertible matrix a be 1, 2 and 4 respectively, then [i-2a ^ - 1] is equal to It's the value of the determinant,

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• 1. It is proved that the necessary and sufficient condition of invertibility of matrix A is that its eigenvalues are not equal to zero
• 2. How to prove that matrix A is invertible if and only if 0 is not the eigenvalue of a GOT IT
• 3. Is the invertibility of (a + b) matrix equal to the invertibility of a + if not, what
• 4. Let 2 be an eigenvalue of invertible matrix A, then an eigenvalue of 3A ^ 2 + e is
• 5. Let the sum of all elements of nonsingular matrix a be 2, then the matrix (1 / 3A ^ 2) ^ - 1 has an eigenvalue equal to () (a) 4 / 3; (b) 3 / 4;
• 6. Let λ = 2 be an eigenvalue of invertible matrix A, then matrix (13a) - 1 must have an eigenvalue equal to______ ．
• 7. There is a m × n matrix A whose rank is n, that is to say, its column vectors are independent. How can we prove that the transpose × a of a is an invertible matrix?
• 8. Let a be an M × n matrix, C be an invertible matrix of order n, the rank of matrix A is r, and the rank of matrix B = AC is R1, then () A. R ＞ r1b. R ＜ r1c. R = r1d. The relationship between R and R1 depends on C
• 9. Why is invertible matrix full rank?
• 10. How to prove that the rank of the sum of two matrices is not less than the sum of matrix ranks rt Hehe, it's the opposite. It should be no more than
• 11. Linear Algebra: there is a problem -- let a = (1,0, - 1) t, matrix A = AAT, n be a positive integer, find the determinant of ae-a ^ n? There is a sentence in the answer: from R (a) = 1, we know that the eigenvalues of a are 2,0,0?
• 12. Let | a | = D ≠ 0 be the determinant of matrix A of order n, and find | a*| Adjoint matrix of a
• 13. If matrix a satisfies: AAT = E and | a | = - 1, then matrix a must have an eigenvalue of - 1. Why is it equal to proving that the determinant of | a + e | is 0
• 14. The rank of matrix A is 1. It is proved that the eigenvalue of a has n-1 zeros? The rank of matrix A is 1. It is proved that the eigenvalue of a has n-1 zeros and another eigenvalue is the sum of diagonal elements Would you like to be more detailed? What does this diagram show?
• 15. Linear Algebra: if the rank r of matrix A of order n
• 16. In linear algebra, what is the relationship between the rank of a matrix and its eigenvalues?
• 17. Linear Algebra: let the eigenvalue of the real symmetric matrix A of order 3 be A1 = - 1, A2 = A3 = 1, and the eigenvector corresponding to A1 be B1 = (0,0,1) t, then calculate the matrix A
• 18. Linear algebra proves that the eigenvectors A1 and A2 corresponding to different eigenvalues of real symmetric matrix a must be orthogonal
• 19. Given the three eigenvalues A1 = 0, A2 = A3 = 2 of the real symmetric matrix A of order 3, and the eigenvector corresponding to the eigenvalue 0 is (1,0, - 1) ^ t, find the matrix A
• 20. Linear Algebra: why is the third order real symmetric matrix A, R (a-2e) = 1, so 2 is the double eigenvalue of a?