GATE Mechanical 2022 Set 2 | Question: 38

Question

If the sum and product of eigenvalues of a $2 \times 2$ real matrix $\begin{bmatrix} 3 & p\\ p & q \end{bmatrix}$ are $4$ and $-1$ respectively, then $\left | p \right |$ is ______________ (in integer).

Answer 1

• Summation of eigen value= trace of matrix
• product of eigen value= determinant of the matrix

its given: $3+q=4\implies q=1$

 also $3q-p^2=-1$

$-p^2=-1-3$

$-p^2=-4$ or $p=\pm2$

so $p=2$ is correct.

Answer 2

|P|= 2, is the correct answer.....here is the Explanation