GATE ECE 2008 | Question: 1

Question

All the four entries of the $2 \times 2$ matrix $\mathbf{P}=\left[\begin{array}{ll}p_{11} & p_{12} \\ p_{21} & p_{22}\end{array}\right]$ are nonzero, and one of its eigenvalues is zero. Which of the following statements is true?

• A. $p_{11} p_{22}-p_{12} p_{21}=1$
• B. $p_{11} p_{22}-p_{12} p_{21}=-1$
• C. $p_{11} p_{22}-p_{12} p_{21}=0$
• D. $p_{11} p_{22}+p_{12} p_{21}=0$

Comments

Answer c

Answer 1

if one of the eigen values is zero then product of eigen values will be zero.
And we know that product of eigen values is determinant of matrix then we can conclude that
p11p11 - p12p21 = 0.

Answer 2

Since the |A|=Product of the Eigen values e1*e2

One of the Eigen value is 0 so |A|=e1*e2=0

|A|=p11.p22-p12.p21=0 so C