The sum of the minor and the cofactor of the element 6 in the determinant vmatrix 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 vmatrix is : Option 1: -5 Option 2: 10 Option 3: 10 Option 4: 0

Answer: 0. Solution: Element 6 is at position (2, 3). Minor M_23 = vmatrix 2 & 3 \\ 7 & 8 vmatrix = 16 - 21 = -5. Cofactor C_23 = (-1)^(2+3) M_23 = -(-5) = 5. Sum = M_23 + C_23 = -5 + 5 = 0.

Applied Mathematics

Algebra

Medium

The sum of the minor and the cofactor of the element 6 in the determinant $\begin{vmatrix} 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$ is :

-5

✅ Correct Option: 4

Element 6 is at position (2, 3).

Minor $M_{23} = \begin{vmatrix} 2 & 3 \\ 7 & 8 \end{vmatrix} = 16 - 21 = -5$ .

Cofactor $C_{23} = (-1)^{2+3} M_{23} = -(-5) = 5$ .

Sum = $M_{23} + C_{23} = -5 + 5 = 0$ .

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Match List I with List II

LIST I	LIST II
A. A matrix that has unequal number of rows and columns is called	I. Non-singular matrix
B. A matrix whose determinant is non-zero is called	II. Null matrix
C. A diagonal matrix whose diagonal elements are equal is called	III. Rectangular matrix
D. A matrix that is both symmetric and skew-symmetric is	IV. Scalar matrix

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The sum of the minor and the cofactor of the element 6 in the determinant ∣231456789∣\begin{vmatrix} 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}​247​358​169​​ is :

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The sum of the minor and the cofactor of the element 6 in the determinant $\begin{vmatrix} 2 & 3 & 1 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{vmatrix}$ is :