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JEE Main 2013 Paper

Section: Mathematics

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Question : 50 of 90

Marks: +1, -0

If

P=\begin{pmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{pmatrix}

is adjacent of a

3 \times 3

|A|=4

,then α is equal to

11
5
0
4

Solution:

Solution:-

P=\begin{vmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{vmatrix}

Solving the determinant, we have

|P| = 1(12-12) - \alpha (4-6) + 3(4-6)

\Rightarrow |P| = 0 - (-2 \alpha) + 3(-2)

|P| = 2\alpha - 6 \;\; \dots (1)

\because P = \operatorname{adj}(A)

(Given)

\therefore |P| = |\operatorname{adj}(A)|

\Rightarrow |P| = |A|^{(3-1)} = 4^{2} ( \because |\operatorname{adj}(A)| = |A|^{(n-1)} ;

whereas

n

is the order of matrix

A )

|P| = 16 \dots (2)

From eq

{}^n(1) \& (2)

, we have

2 \alpha - 6 = 16

2 \alpha = 22

\Rightarrow \alpha = 11

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