![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
On the adjoint matrix |(1 2) (3 4)| A11=(-1)^2*4=4 A12=(-1)^3*3=-3 A21=(-1)^3*2=-2 A22=(-1)^4*1=1 Why is its adjoint matrix not | (4 - 3) (- 21) |, but | (4 - 2) (- 31) |?
The adjoint matrix of matrix A is the "transpose matrix" of the algebraic co submatrix of a (where a is a matrix of second order or greater)
Note: transpose matrix
What is the adjoint matrix?
The adjoint matrix of a is formed by transposing the algebraic cofactors of the elements of a matrix into a new matrix
The algebraic cofactor of an element is the determinant of the matrix formed by removing the row and column elements of an element in the matrix, and then multiplied by the power of - 1 (number of rows + number of columns)
RELATED INFORMATIONS
- 1. The problem of line generation adjoint matrix If a is an invertible matrix of order n and a * is an adjoint matrix of a, then (a *) * = () A ㄧAㄧ^n-1 A B ㄧAㄧ^n-2 A C ㄧAㄧ^n+1 A D ㄧAㄧ^n+2 A Don't just choose the answer of ABCD, explain the detailed process, answer the detailed and clear additional bonus points, thank you!
- 2. A is the matrix (1 / 2 - 3 ^ (1 / 2); (3 ^ (1 / 2)) / 4 1 / 2) 1.A^6=E 2. If a ^ n = an * a + BN * e, find an, BN Can you do the second question without Hamilton method?
- 3. Finding the rank of matrix (2 - 1 - 1 1 2) (1 1 - 2 1 4) (4 - 6 2) by matrix transformation- Finding the rank of matrix by matrix transformation （2 -1 -1 1 2） （1 1 -2 1 4） （4 -6 2 -2 4） （3 6 -9 7 9） How to find rank, some matrix transformation is hard to think of
- 4. 1. What is the essence of elementary transformation of matrix? 2. How many kinds of elementary transformation?
- 5. 1.x²+4x-5=0 2.x²=5x-4
- 6. Use the elementary row transformation method to find the inverse matrix of the following matrix A: the first row (3.2.0.0), the second row (4.5.0.0), the third row (0.0.4.1) and the fourth row (0.0.6.2)
- 7. Using the elementary transformation method to find the inverse matrix of the matrix, the first line is 12-1, the second line is 34-2, and the third line is 5-41
- 8. The first row is 1,2,3,4, the second row is 0,1,2,3, the third row is 0,0,1,2, the fourth row is 0,0,0,1. By using the elementary row transformation method, the inverse matrix of the invertible matrix is obtained,
- 9. Is this a ladder matrix? 1 2 3 4 0 2 3 4 0 4 5 6 0 6 7
- 10. 2, - 1. - 1,1,2,1,1, - 2.1,4, - 6,2, - 2,4,3,6, - 9,7,9 to the row simplest form matrix needs a process of five numbers What is the largest unrelated group?
- 11. When matrix A is inversed [2 - 1 line feed - 5 3] | e line transform becomes e | A-1, and the first line is extracted twice, it becomes 2 [1 - 1 / 2 line feed - 5]
- 12. Matrix 200 line feed 0 2 3 line feed 0 3 2 eigenvalue eigenvector
- 13. It is proved that if α and β are orthogonal, then K α and l β are also orthogonal for any real number k and L
- 14. In linear algebra, we know that a and B are n-order matrices, and E-Ab is invertible. How can we prove that e-Ba is also invertible?
- 15. Block matrix problem Matrix (o a) How to find the inverse matrix of B (o)? A is a matrix of order n, B is a matrix of order s, a and B are invertible
- 16. ( 0 -2 0) A = ( -4 1 4) ( 2 5 -2) 3 × 3 matrix The eigenvalues are 0,5 and - 6 How to find the corresponding unit eigenvectors
- 17. Who knows the problem of matrix, Let a be a symmetric matrix of order n and B be an anti Chen matrix of order n It is proved that: 1. B ^ 2 (the square of B) is a symmetric matrix; 2. Ab-ba is a symmetric matrix and ab + Ba is an antisymmetric matrix
- 18. Java simple two dimensional array exercises Using two-dimensional array to achieve the following graphics output * *** *** * Want to use two-dimensional array, nested loop also need two-dimensional array assignment, nested loop will not use it, please write it down
- 19. Let a = (α, 2, γ 1, 3, γ 2), B = (β, γ 1, γ 2), where α, β, γ 1, γ 2 are three-dimensional column vectors, | a | = 15, | B | = 2, find | a-b| Let a = (α, 2, γ 1, 3, γ 2), B = (β, γ 1, γ 2), where α, β, γ 1, γ 2 are three-dimensional column vectors, | a | = 18, | B | = 2, find | a-b|
- 20. Let a = (α, γ 2, γ 3) and B = (β, γ 2, γ 3), where α, β, γ 2 and γ 3 are all ternary matrices Let a = (α, γ 2, γ 3) and B = (β, γ 2, γ 3), where α, β, γ 2 and γ 3 are all ternary matrix, and | a | = 2 and | B | = 1 / 2 are known, then | a + B is obtained|