The value of the determinant 1 beginvmatrix log - a frac x y -log - a frac y z -log - a frac z x l -log - b frac y z -log - b z x -log - b frac x y log - clfraczx -log - cfracxy -log - cfracyzlend vmatrix isA- -1B- 1C- None of theseD- log c x y z

The correct option is C None of theseApplying C_1 → C_1+C_2 +C_3 Then, 0 amp; log_a(y/z) amp; log_a(z/x) 0 amp; log_b(z/x) amp; log_b(x/y) 0 ...

You visited us 64 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties of Determinants

The value of ...

Question

The value of the determinant $∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} l o g_{a} (\frac{x}{y}) & l o g_{a} (\frac{y}{z}) & l o g_{a} (\frac{z}{x}) l o g_{b} (\frac{y}{z}) & l o g_{b} (\frac{z}{x}) & l o g_{b} (\frac{x}{y}) l o g_{c} (\frac{z}{x}) & l o g_{c} (\frac{x}{y}) & l o g_{c} (\frac{y}{z}) \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣$ is

No worries! We‘ve got your back. Try BYJU‘S free classes today!

-1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

l o g_{c} x y z

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D None of these
Applying $C_{1} \to C_{1} + C_{2} + C_{3}$
Then, $∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 0 & l o g_{a} (\frac{y}{z}) & l o g_{a} (\frac{z}{x}) 0 & l o g_{b} (\frac{z}{x}) & l o g_{b} (\frac{x}{y}) 0 & l o g_{c} (\frac{x}{y}) & l o g_{c} (\frac{y}{z}) \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ = 0$

Suggest Corrections

Similar questions

For positive numbers x, y and z the numerical value of the following determinant

$∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & {l o g}_{x} y & {l o g}_{x} z {l o g}_{y} x & 1 & {l o g}_{y} z {l o g}_{z} x & {l o g}_{z} y & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣$ is

Q. For positive numbers x, y and z the numerical value of the determinant

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & l o g_{x} y & l o g_{x} z l o g_{y} x & 1 & l o g_{y} z l o g_{z} x & l o g_{z} y & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

Q. For positive numbers x, y and z, the numerical value of the determinant

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & l o g_{x} y & l o g_{x} z l o g_{y} x & 1 & l o g_{y} z l o g_{z} x & l o g_{z} y & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

is ___

The value of the determinant
$Δ = ∣ ∣ ∣ ∣ \begin{matrix} l o g x & l o g y & l o g z l o g 2 x & l o g 2 y & l o g 2 z l o g 3 x & l o g 3 y & l o g 3 z \end{matrix} ∣ ∣ ∣ ∣$ is

Join BYJU'S Learning Program

The value of the determinant ∣∣ ∣ ∣ ∣∣loga(xy)loga(yz)loga(zx)logb(yz)logb(zx)logb(xy)logc(zx)logc(xy)logc(yz)∣∣ ∣ ∣ ∣∣ is

The correct option is D None of theseApplying C1→C1+C2+C3 Then, ∣∣ ∣ ∣ ∣∣0loga(yz)loga(zx)0logb(zx)logb(xy)0logc(xy)logc(yz)∣∣ ∣ ∣ ∣∣=0