Let a - 2 b + c = 1 . If f x = x + a x + 2 x + 1 x + b x + 3 x + 2 x + c x + 4 x + 3 , then:

Apply R 1 = R 1 + R 3 - 2 R 2 ⇒ f x = a - 2 b + c 1 0 0 x + b x + 3 x + 2 x + c x + 4 x + 3 ⇒ f x = 1 x + 3 2 - x + 2 x + 4 ⇒ f x = 1 ⇒ f 50 = 1

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Mathematics - Determinant Question with Solution | TestHub

MathematicsDeterminantProperties of det.Easy2 minPYQ_2020

MathematicsEasysingle choice

Let $a - 2 b + c = 1 .$
If $f (x) = |\begin{matrix} x + a & x + 2 & x + 1 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{matrix}|,$ then:

Options:

Answer:

Solution:

Apply $R_{1} = R_{1} + R_{3} - 2 R_{2}$
$\Rightarrow f (x) = (a - 2 b + c) |\begin{matrix} 1 & 0 & 0 \\ x + b & x + 3 & x + 2 \\ x + c & x + 4 & x + 3 \end{matrix}|$

$\Rightarrow f (x) = 1 [{(x + 3)}^{2} - (x + 2) (x + 4)]$

$\Rightarrow f (x) = 1$

$\Rightarrow f (50) = 1$

Stream:JEESubject:MathematicsTopic:DeterminantSubtopic:Properties of det.

⏱ 2mℹ️ Source: PYQ_2020

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