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If a is square matrix of order 3 and Aij and cofactor of element Aij then value of?
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If a is square matrix of order 3 and Aij and cofactor of element Aij t...
Introduction:
In linear algebra, the cofactor of an element in a square matrix is a key concept. It is directly related to the determinant of the matrix and can be used to find the inverse of the matrix. In this case, we have a square matrix of order 3, denoted as A, and we need to find the value of the cofactor Aij.
Explanation:
To understand the concept of cofactors, we first need to understand the concept of minors. The minor of an element Aij in a matrix A is the determinant of the submatrix obtained by deleting the ith row and jth column of A. Let's denote the minor of Aij as Mij.
Formula for Cofactor:
The cofactor of an element Aij is given by the formula:
Cij = (-1)^(i + j) * Mij
Steps to Find the Cofactor:
1. Find the minor Mij by deleting the ith row and jth column of the matrix A.
2. Calculate the cofactor Cij using the formula mentioned above.
Application to Matrix A:
Since we have a square matrix of order 3, we need to find the cofactor Aij for each element Aij in the matrix A. Let's denote the elements of the matrix A as A11, A12, A13, A21, A22, A23, A31, A32, and A33.
1. Cofactor of A11: Calculate the minor M11 by deleting the 1st row and 1st column of matrix A. Then, use the formula to find the cofactor C11.
2. Cofactor of A12: Calculate the minor M12 by deleting the 1st row and 2nd column of matrix A. Then, use the formula to find the cofactor C12.
3. Cofactor of A13: Calculate the minor M13 by deleting the 1st row and 3rd column of matrix A. Then, use the formula to find the cofactor C13.
4. Cofactor of A21: Calculate the minor M21 by deleting the 2nd row and 1st column of matrix A. Then, use the formula to find the cofactor C21.
5. Cofactor of A22: Calculate the minor M22 by deleting the 2nd row and 2nd column of matrix A. Then, use the formula to find the cofactor C22.
6. Cofactor of A23: Calculate the minor M23 by deleting the 2nd row and 3rd column of matrix A. Then, use the formula to find the cofactor C23.
7. Cofactor of A31: Calculate the minor M31 by deleting the 3rd row and 1st column of matrix A. Then, use the formula to find the cofactor C31.
8. Cofactor of A32: Calculate the minor M32 by deleting the 3rd row and 2nd column of matrix A. Then, use the formula to find the cofactor C32.
9. Cofactor of A33: Calculate the minor M33 by deleting the 3rd row and 3rd column of matrix A. Then, use the formula to find the cofactor C33.
Conclusion
In linear algebra, the cofactor of an element in a square matrix is a key concept. It is directly related to the determinant of the matrix and can be used to find the inverse of the matrix. In this case, we have a square matrix of order 3, denoted as A, and we need to find the value of the cofactor Aij.
Explanation:
To understand the concept of cofactors, we first need to understand the concept of minors. The minor of an element Aij in a matrix A is the determinant of the submatrix obtained by deleting the ith row and jth column of A. Let's denote the minor of Aij as Mij.
Formula for Cofactor:
The cofactor of an element Aij is given by the formula:
Cij = (-1)^(i + j) * Mij
Steps to Find the Cofactor:
1. Find the minor Mij by deleting the ith row and jth column of the matrix A.
2. Calculate the cofactor Cij using the formula mentioned above.
Application to Matrix A:
Since we have a square matrix of order 3, we need to find the cofactor Aij for each element Aij in the matrix A. Let's denote the elements of the matrix A as A11, A12, A13, A21, A22, A23, A31, A32, and A33.
1. Cofactor of A11: Calculate the minor M11 by deleting the 1st row and 1st column of matrix A. Then, use the formula to find the cofactor C11.
2. Cofactor of A12: Calculate the minor M12 by deleting the 1st row and 2nd column of matrix A. Then, use the formula to find the cofactor C12.
3. Cofactor of A13: Calculate the minor M13 by deleting the 1st row and 3rd column of matrix A. Then, use the formula to find the cofactor C13.
4. Cofactor of A21: Calculate the minor M21 by deleting the 2nd row and 1st column of matrix A. Then, use the formula to find the cofactor C21.
5. Cofactor of A22: Calculate the minor M22 by deleting the 2nd row and 2nd column of matrix A. Then, use the formula to find the cofactor C22.
6. Cofactor of A23: Calculate the minor M23 by deleting the 2nd row and 3rd column of matrix A. Then, use the formula to find the cofactor C23.
7. Cofactor of A31: Calculate the minor M31 by deleting the 3rd row and 1st column of matrix A. Then, use the formula to find the cofactor C31.
8. Cofactor of A32: Calculate the minor M32 by deleting the 3rd row and 2nd column of matrix A. Then, use the formula to find the cofactor C32.
9. Cofactor of A33: Calculate the minor M33 by deleting the 3rd row and 3rd column of matrix A. Then, use the formula to find the cofactor C33.
Conclusion
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If a is square matrix of order 3 and Aij and cofactor of element Aij then value of?
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If a is square matrix of order 3 and Aij and cofactor of element Aij then value of? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If a is square matrix of order 3 and Aij and cofactor of element Aij then value of? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a is square matrix of order 3 and Aij and cofactor of element Aij then value of?.
If a is square matrix of order 3 and Aij and cofactor of element Aij then value of? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about If a is square matrix of order 3 and Aij and cofactor of element Aij then value of? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If a is square matrix of order 3 and Aij and cofactor of element Aij then value of?.
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