If- 6i -3i 1 4 3i -1 20 3 i - -x -y i then find the value of x- y

| 6i amp; 3i amp; 1 4 amp; 3i amp; 1 20 amp; 3 amp; i |=x+iy C_1→C_1 3i ⇒ 3i| 6i amp; 1 amp; 1 4 ...

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Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

If| 6i -3i ...

Question

$I f ∣ ∣ ∣ ∣ \begin{matrix} 6 i & - 3 i & 1 4 & 3 i & - 1 20 & 3 & i \end{matrix} ∣ ∣ ∣ ∣ = x + y i$ then find the value of ( x, y)

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Solution

$∣ ∣ ∣ ∣ \begin{matrix} 6 i & - 3 i & 1 4 & 3 i & - 1 20 & 3 & i \end{matrix} ∣ ∣ ∣ ∣ = x + i y$
$C_{1} \to \frac{C_{1}}{- 3 i}$
$\Rightarrow - 3 i ∣ ∣ ∣ ∣ \begin{matrix} 6 i & 1 & 1 4 & - 1 & - 1 20 & i & i \end{matrix} ∣ ∣ ∣ ∣ = x + i y$
Since $C_{2} = C_{3}$ we have $Δ = 0$
$\Rightarrow x + i y = 0$
$∴ (x, y) = (0, 0)$

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If∣∣ ∣∣6i−3i143i−1203i∣∣ ∣∣=x+yi then find the value of ( x, y)

∣∣ ∣∣6i−3i143i−1203i∣∣ ∣∣=x+iyC1→C1−3i⇒−3i∣∣ ∣∣6i114−1−120ii∣∣ ∣∣=x+iySince C2=C3 we have Δ=0⇒x+iy=0∴(x,y)=(0,0)

$I f ∣ ∣ ∣ ∣ \begin{matrix} 6 i & - 3 i & 1 4 & 3 i & - 1 20 & 3 & i \end{matrix} ∣ ∣ ∣ ∣ = x + y i$ then find the value of ( x, y)