Search any question & find its solution
Question:
Answered & Verified by Expert
If $\left|\begin{array}{ccc}a^{2} & b c & c^{2}+a c \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right|=k a^{2} b^{2} c^{2}$, then $k=$
Options:
Solution:
1909 Upvotes
Verified Answer
The correct answer is:
4
Hint:
$\left|\begin{array}{ccc}a^{2} & b c & c^{2}+a c \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right|=(a b c)\left|\begin{array}{ccc}a & c & a+c \\ a+b & b & a \\ b & b+c & c\end{array}\right|$
opening through $\mathrm{R}-1=4 \mathrm{a}^{2} \mathrm{~b}^{2} \mathrm{C}^{2}$
$\left|\begin{array}{ccc}a^{2} & b c & c^{2}+a c \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right|=(a b c)\left|\begin{array}{ccc}a & c & a+c \\ a+b & b & a \\ b & b+c & c\end{array}\right|$
opening through $\mathrm{R}-1=4 \mathrm{a}^{2} \mathrm{~b}^{2} \mathrm{C}^{2}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.