The value of determinant 1111123413610141020 is -

The correct option is D 1We nbsp;have nbsp;1111123413610141020On nbsp;applying nbsp;R2→R2 R1,R3→R3 R1,R4→R4 R1,we nbsp;get 11110123025903919=123259391 ...

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Byju's Answer

Standard XII

Mathematics

Properties of Determinants

The value of ...

Question

The value of determinant $⎛ ⎜ ⎜ ⎜ ⎝ \begin{matrix} 1 & 1 & 1 & 1 1 & 2 & 3 & 4 1 & 3 & 6 & 10 1 & 4 & 10 & 20 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$ is .

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Solution

The correct option is D 1
$We have$ $⎛ ⎜ ⎜ ⎜ ⎝ \begin{matrix} 1 & 1 & 1 & 1 1 & 2 & 3 & 4 1 & 3 & 6 & 10 1 & 4 & 10 & 20 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ On applying R_{2} \to R_{2} - R_{1}, R_{3} \to R_{3} - R_{1}, R_{4} \to R_{4} - R_{1}, we get - ⎛ ⎜ ⎜ ⎜ ⎝ \begin{matrix} 1 & 1 & 1 & 1 0 & 1 & 2 & 3 0 & 2 & 5 & 9 0 & 3 & 9 & 19 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ = ⎛ ⎜ ⎝ \begin{matrix} 1 & 2 & 3 2 & 5 & 9 3 & 9 & 19 \end{matrix} ∣ ∣ ∣ ∣ On applying R_{2} \to R_{2} - 2 R_{1}, R_{3} \to R_{3} - 3 R_{1}, we get - ⎛ ⎜ ⎝ \begin{matrix} 1 & 2 & 3 0 & 1 & 3 0 & 3 & 10 \end{matrix} ∣ ∣ ∣ ∣ = 1 (10 - 9) = 1$

Suggest Corrections

The value of determinant ⎛⎜ ⎜ ⎜⎝1111123413610141020∣∣ ∣ ∣ ∣∣ is .

The value of determinant $⎛ ⎜ ⎜ ⎜ ⎝ \begin{matrix} 1 & 1 & 1 & 1 1 & 2 & 3 & 4 1 & 3 & 6 & 10 1 & 4 & 10 & 20 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$ is .