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The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the
- a)jth row of the determinant
- b)ith column and jth row of the determinant
- c)ith row and jth column of the determinant
- d)ith row of the determinant
Correct answer is option 'C'. Can you explain this answer?
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The minor Mijof an element aijof a determinant is defined as the value...
A minor, Mij, of the element aij is the determinant of the matrix obtained by deleting the ith row and jth column.
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The minor Mijof an element aijof a determinant is defined as the value...
Explanation:
The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the ith row and jth column of the determinant. This means that the minor Mij is a square matrix of order n-1, where n is the order of the original determinant.
For example, consider a determinant A of order 4x4. Let aij be an element of A. Then the minor Mij of aij is obtained by deleting the ith row and jth column of A, resulting in a 3x3 matrix.
To find the minor Mij, we need to follow these steps:
1. Identify the element aij in the determinant A.
2. Delete the ith row and jth column of A to obtain a new matrix B.
3. Calculate the determinant of B.
4. The determinant of B is the minor Mij of aij.
For example, let's find the minor M23 of the following determinant A:
A = | 1 2 3 |
| 4 5 6 |
| 7 8 9 |
1. Identify the element a23 in A, which is 6.
2. Delete the 2nd row and 3rd column of A to obtain a new matrix B:
B = | 1 2 |
| 7 8 |
3. Calculate the determinant of B:
det(B) = (1*8) - (2*7) = -6
4. The determinant of B is the minor M23 of a23, which is -6.
Therefore, the answer is option C, which states that the minor Mij is obtained by deleting the ith row and jth column of the determinant.
The minor Mij of an element aij of a determinant is defined as the value of the determinant obtained after deleting the ith row and jth column of the determinant. This means that the minor Mij is a square matrix of order n-1, where n is the order of the original determinant.
For example, consider a determinant A of order 4x4. Let aij be an element of A. Then the minor Mij of aij is obtained by deleting the ith row and jth column of A, resulting in a 3x3 matrix.
To find the minor Mij, we need to follow these steps:
1. Identify the element aij in the determinant A.
2. Delete the ith row and jth column of A to obtain a new matrix B.
3. Calculate the determinant of B.
4. The determinant of B is the minor Mij of aij.
For example, let's find the minor M23 of the following determinant A:
A = | 1 2 3 |
| 4 5 6 |
| 7 8 9 |
1. Identify the element a23 in A, which is 6.
2. Delete the 2nd row and 3rd column of A to obtain a new matrix B:
B = | 1 2 |
| 7 8 |
3. Calculate the determinant of B:
det(B) = (1*8) - (2*7) = -6
4. The determinant of B is the minor M23 of a23, which is -6.
Therefore, the answer is option C, which states that the minor Mij is obtained by deleting the ith row and jth column of the determinant.
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The minor Mijof an element aijof a determinant is defined as the value of the determinant obtained after deleting thea)jthrow of the determinantb)ithcolumn and jth row of the determinantc)ithrow and jthcolumn of the determinantd)ithrow of the determinantCorrect answer is option 'C'. Can you explain this answer?
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The minor Mijof an element aijof a determinant is defined as the value of the determinant obtained after deleting thea)jthrow of the determinantb)ithcolumn and jth row of the determinantc)ithrow and jthcolumn of the determinantd)ithrow of the determinantCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The minor Mijof an element aijof a determinant is defined as the value of the determinant obtained after deleting thea)jthrow of the determinantb)ithcolumn and jth row of the determinantc)ithrow and jthcolumn of the determinantd)ithrow of the determinantCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minor Mijof an element aijof a determinant is defined as the value of the determinant obtained after deleting thea)jthrow of the determinantb)ithcolumn and jth row of the determinantc)ithrow and jthcolumn of the determinantd)ithrow of the determinantCorrect answer is option 'C'. Can you explain this answer?.
The minor Mijof an element aijof a determinant is defined as the value of the determinant obtained after deleting thea)jthrow of the determinantb)ithcolumn and jth row of the determinantc)ithrow and jthcolumn of the determinantd)ithrow of the determinantCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The minor Mijof an element aijof a determinant is defined as the value of the determinant obtained after deleting thea)jthrow of the determinantb)ithcolumn and jth row of the determinantc)ithrow and jthcolumn of the determinantd)ithrow of the determinantCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minor Mijof an element aijof a determinant is defined as the value of the determinant obtained after deleting thea)jthrow of the determinantb)ithcolumn and jth row of the determinantc)ithrow and jthcolumn of the determinantd)ithrow of the determinantCorrect answer is option 'C'. Can you explain this answer?.
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