All lines are added to the first line, and the common factor (λ+4) is proposed, and the first line becomes all elements 1.

Then subtract the first line from the second, third and fourth lines, so that the second, third and fourth lines are all zero except the diagonal element λ.

The value of determinant is (λ+4) λ 3 = 0.

The roots of this equation are λ 1=λ2=λ3=0, λ4=-4.