Ques. -6

Algebra Level 3

$\left | \begin{array}{ccc} e^a & e^{2a} & (e^{3a}-1) \\ e^b & e^{2b} & (e^{3b}-1) \\ e^c & e^{2c} & (e^{3c}-1) \\ \end{array} \right |$

if $a,b$ and $c$ are cube roots of unity, find the determinant of the matrix above.

e^2

e^3

1 solution

Raghav Vaidyanathan
Mar 2, 2015

First put $a=1, b=\omega ,c={ \omega }^{ 2 }$ . Let value of this determinant to be $A$ .

Then put $a={ \omega }^{ 2 },b=\omega,c=1$ . Let value of this determinant to be $B$ .

$A=B=-A\Rightarrow A=0$

Classic JEE style.

Just the thing I did ;)

Saswata Dasgupta - 6 years, 2 months ago

Yeahbsolutely ;)

Siddharth Bhatnagar - 6 years, 2 months ago