Multiple choice

All the four entries of the 2 x 2 matrix = $\begin{bmatrix} \ p11 & p12 \ \ p21 & p22 \ \end{bmatrix}$ matrix are non-zero, and one of its eigen value is zero. Which of the following statements is true?

  1. p11p12 - p12p21 = 1

  2. p11p22 - p12p21 = -1

  3. p11p22 - p12p21 = 0

  4. p11p22 + p12p21 = 0

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The product of Eigen value is equal to the determinant of the matrix. Since one of the Eigen value is zero, the product of Eigen value is zero, thus determinant of the matrix is zero. Thus p11 p22 - p12 p21 = 0