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Mathematics · JEE | DETERMINANTS
हिन्दीMatch List-I with List-II: List-I List-II A Minor \( M_{ij} \) of element \( a_{ij} \) I \( (-1)^{i+j} M_{ij} \) B Cofactor \( A_{ij} \) of element \( a_{ij} \) II Determinant obtained by deleting \( i^{\text{th}} \) row and \( j^{\text{th}} \) column C Area of triangle with vertices \( (x_i, y_i) \) III \( k^n |A| \) for matrix of order \( n \) D Determinant of scalar multiple \( |kA| \) IV \( \frac{1}{2} \begin{vmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{vmatrix} \) (absolute value) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I | List-II | ||
|---|---|---|---|
| A | Minor \( M_{ij} \) of element \( a_{ij} \) | I | \( (-1)^{i+j} M_{ij} \) |
| B | Cofactor \( A_{ij} \) of element \( a_{ij} \) | II | Determinant obtained by deleting \( i^{\text{th}} \) row and \( j^{\text{th}} \) column |
| C | Area of triangle with vertices \( (x_i, y_i) \) | III | \( k^n |A| \) for matrix of order \( n \) |
| D | Determinant of scalar multiple \( |kA| \) | IV | \( \frac{1}{2} \begin{vmatrix} x_1 & y_1 & 1 \ x_2 & y_2 & 1 \ x_3 & y_3 & 1 \end{vmatrix} \) (absolute value) |
Choose the correct answer from the options given below:
View Answer & Solution
Correct answer · Option B
A-(II), B-(I), C-(IV), D-(III)
Explanation
By matching definitions: Minor is determinant after deleting row/col (II), Cofactor is signed minor (I), Area of triangle uses half-determinant absolute value (IV), and scalar determinant property is \( k^n |A| \) (III).
