Pick the odd one out.Question 4Select one:𝜆 is a solution of the characteristic equation 𝑑𝑒𝑡 (𝜆𝐼 - 𝐴) = 0.𝜆 is an eigen value of A.There is a nonzero vector x such that 𝐴𝑥 = 𝜆𝑥.The system of equations (𝜆𝐼 - 𝐴)𝑥 = 0 has trivial solutions.

Let 𝜆 is an Eigen value of a 𝑛 × 𝑛 𝑚𝑎𝑡𝑟𝑖𝑥 𝐴.

Which of the following is true for matrices?Question 1Select one: (𝐴𝑇) = 𝐴 (𝐴𝐵)-1 = 𝐵-1𝐴-1 𝐴*𝐼 = 𝐴𝐴𝐵=𝐵𝐴

If 0 is an Eigen value of a matrix A, then the set of columns of A isQuestion 5Select one:Linearly independent always.Linearly independent or linearly dependent..Cannot be determined.Linearly dependent always.

Let A=【3 2 4 2 0 2 4 2 3】 You are given that the characteristic equation of A is (λ + 1)2(λ − 8) = 0, i.e. the eigenvalues of A are λ = −1, 8. Are the eigenvectors of A corresponding to the eigenvalue λ = −1 orthogonal with respect to the usual dot product? If not, apply the Gram-Schmidt process to turn them into an orthonormal set of eigenvectors

The equationsin(xy)(dydx)3+2x=0sin⁡(𝑥𝑦)(𝑑𝑦𝑑𝑥)3+2𝑥=0is a Question 38Select one:a.None of the othersb.Separable differential equationc.Third order differential equationd.Second order differential equatione.First order differential equation