The co-factor of the element -4- in the determinant - 1 3 5 1 2 3 4 2 8 0 1 1 0 2 1 1 - is

The correct option is B 10 Here a_23=4 Cofactor c_ij=( 1)^I+jM_ij M_23= 1 amp; 3 amp; 5 amp; 1 2 amp; 3 amp; 4 amp; 2 ...

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Byju's Answer

Standard XII

Mathematics

Finding Inverse Using Elementary Transformations

The co-factor...

Question

The co-factor of the element $^{'} 4^{'}$ in the determinant $∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 3 & 5 & 1 2 & 3 & 4 & 2 8 & 0 & 1 & 1 0 & 2 & 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$ is

4

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10

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- 10

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- 4

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Solution

The correct option is B $10$
Here $a_{23} = 4$
Cofactor $c_{i j} = (- 1)^{I + j} M_{i j}$
$M_{23} = ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 3 & 5 & 1 2 & 3 & 4 & 2 8 & 0 & 1 & 1 0 & 2 & 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$
$C_{23} = (- 1)^{2 + 3} M 23 = (- 1)^{5} ∣ ∣ ∣ ∣ \begin{matrix} 1 & 3 & 1 8 & 0 & 1 0 & 2 & 1 \end{matrix} ∣ ∣ ∣ ∣$
$= - [1 (0 - 2) - 3 (8 - 0) + 1 (16 - 0)]$
$= - [- 2 - 24 + 16] = 10$ .

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The co-factor of the element ′4′ in the determinant ∣∣ ∣ ∣ ∣∣1351234280110211∣∣ ∣ ∣ ∣∣ is

The correct option is B 10Here a23=4Cofactor cij=(−1)I+jMijM23=∣∣ ∣ ∣ ∣∣1351234280110211∣∣ ∣ ∣ ∣∣C23=(−1)2+3M23=(−1)5∣∣ ∣∣131801021∣∣ ∣∣=−[1(0−2)−3(8−0)+1(16−0)]=−[−2−24+16]=10.

The co-factor of the element $^{'} 4^{'}$ in the determinant $∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 3 & 5 & 1 2 & 3 & 4 & 2 8 & 0 & 1 & 1 0 & 2 & 1 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$ is