If x-1 amp- 3 amp- 5- 2 amp- x-2 amp- 5- 2 amp- 3 amp- x-4 -0- then x -1-9-1-91-9-1-9

The correct option is C 1, 9By C_1→ C_1+C_2+C_3, we have (9+x) x+1 amp; 3 amp; 5 2 amp; x+2 amp; 5 2 amp; 3 amp; x+4 =0 ⇒ (x+9) 0 amp; 1 ...

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Byju's Answer

Standard XII

Mathematics

Properties of Determinants

If x+1 amp...

Question

If $∣ ∣ ∣ ∣ \begin{matrix} x + 1 & 3 & 5 2 & x + 2 & 5 2 & 3 & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = 0,$ then x =

1,9

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-1,9

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-1,-9

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1,-9

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Solution

The correct option is D 1,-9
By $C_{1} \to C_{1} + C_{2} + C_{3},$
we have $(9 + x) ∣ ∣ ∣ ∣ \begin{matrix} x + 1 & 3 & 5 2 & x + 2 & 5 2 & 3 & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow (x + 9) ∣ ∣ ∣ ∣ \begin{matrix} 0 & 1 - x & 0 0 & - (1 - x) & 1 - x 1 & 3 & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow (x + 9) (1 - x)^{2} ∣ ∣ ∣ ∣ \begin{matrix} 0 & 1 & 0 0 & - 1 & 1 1 & 3 & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow x = 1, 1, - 9,$ (Since the determinant = 1).

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Q. If

∣ ∣ ∣ ∣ \begin{matrix} x + 1 & 3 & 5 2 & x + 2 & 5 2 & 3 & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = 0,

then x =

Q. prove that

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If ∣∣ ∣∣x+1352x+2523x+4∣∣ ∣∣=0, then x =

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If $∣ ∣ ∣ ∣ \begin{matrix} x + 1 & 3 & 5 2 & x + 2 & 5 2 & 3 & x + 4 \end{matrix} ∣ ∣ ∣ ∣ = 0,$ then x =