GO Classes 2024 | Weekly Quiz 7 | Linear Algebra | Question: 17

Answer 1

The product of the eigenvalues is $\operatorname{det} A=\operatorname{det} B \times \operatorname{det} C$. $B$ and $C$ are triangular matrices so their determinants are just the products of their diagonals $=1 \times 2 \times 2=4$, hence $\operatorname{det} A=4^2=16$.

Comments

Sir, I did understand the problem and the concept that was applied here.....But what i did not understand was that why is the matrix C given in that manner...

I mean matrix C is the resultant of transpose of B. But the principle diagonal is shown to be different...?

Is it just a distraction for the actual question?