Find the value of 𝜆 that makes the determinant 0. | 𝜆 +2 2| second-row -> |1 𝜆 |

Question

Find the value of 𝜆 that makes the determinant 0. | 𝜆 +2 2|

| 1 𝜆 |

Answer 1

The 2 by 2 determinant is given by subtracting the product of its diagonal, which is:

det = λ(λ+2) - 2 =0 which is to solve the quadratic equation: λ² +2λ - 2=0, which yields the following roots:

λ = -1 - √3 and λ= -1 + √3.