Det formula of matrix determinant How to find the value of matrix determinant?
Is to find the value of the determinant
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- 1. A B C D is a matrix, where a C is a diagonal matrix. Is the value of the determinant det ([a B; C D]) equal to the determinant det (a) * det (d) - det (b) * det (c)
- 2. Let d = | a - 580A + 1803a + 325 | = 0, and let a have three Let d = |a - 580A + 1803a + 325 | = 0 be the determinant of the third order, and a matrix of the third order has three eigenvalues 1 - 10 corresponding to three eigenvectors B1 = (12a - 1) TB2 = (a + 3A + 2) Tb3 = (A-2 - 1A + 1) t to determine the parameter a and find a
- 3. If the eigenvalue of the third-order square matrix A is known to be 1 (double), - 1, then the determinant of a & # 178; + 3A + 2E =?
- 4. If the eigenvalue of a square matrix of order 2 is 1, - 1 and a * is its adjoint matrix, then the value of determinant | a * - 2e | is?
- 5. Let [a] = 2, and a * be its adjoint matrix, then [a *] =?
- 6. Is there any relationship between the value of a matrix and the determinant value of its adjoint matrix? The relationship between a * and a
- 7. Is there any internal relation between the rank of matrix and the rank of vector group?
- 8. The product of matrix and its transpose matrix is zero matrix, and it is proved that the original matrix is zero matrix
- 9. If two matrices are of the same type and of the same rank, can we deduce that they are equivalent
- 10. Let a be an M * n matrix, we prove that there exists an n-order matrix B ≠ 0, so that ab = 0 if and only if R (a)
- 11. Given that a is a real symmetric matrix of order 3, satisfying a ^ 4 + 2A ^ 3 + A ^ 2 + 2A = 0 and rank r (a) = 2, find all eigenvalues of matrix A and rank r (a + e) I can find out the eigenvalue of matrix A is 0 or - 2, but the answer is that because the real symmetric matrix must be similar diagonalized and the rank r (a) = R (similar diagonalization sign) = 2, so the eigenvalues of a are 0, - 2, - 2
- 12. It is known that the third order matrix a satisfies the condition | e-A | = | 2e-a | = | 3e-a | to find the value of determinant | a |
- 13. Find the rank of matrix A = (1000 120 - 13 - 104 145 1) Finding matrix A= 1 0 0 0 1 2 0 -1 3 -1 0 4 1 4 5 1 The rank of
- 14. How to find the rank of this matrix? 1 -a -b -c 0 0
- 15. How to find the rank of matrix
- 16. Find the rank of matrix A = (1,1,2,2,1; 0,2,1,5, - 1; 2,0,3, - 1,3; 1,1,0,4, - 1)
- 17. A is a square matrix of order 4, R (a) is equal to 4
- 18. If the rank of a square matrix of order 4 is 2, what is the rank of its adjoint matrix?
- 19. Let a be a real matrix of order n and a ^ t be a transpose matrix of order A. It is proved that R (a) = R (a ^ TA) Even give 100 points for the answer
- 20. If a and B of the same type have the same rank, then R (a) = R (b) = R (a,