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

The eigen value of ⎡⎣⎢111111111⎤⎦⎥[111111111]  are

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 𝐴 𝑏𝑒 𝑎𝑛 𝑛 × 𝑛 matrix. The characteristic polynomial of A is a polynomial of degree

Prove that: ∫ √sin 𝜃 𝑑𝜃𝜋20 × ∫ 𝑑𝜃√sin 𝜃𝜋20 = 𝜋

Consider the following matrix.A = 23 12 −36 −19Find the eigenvalues and associated eigenvectors of A. (Arrange the eigenvalues so that 𝜆1 < 𝜆2.)𝜆1 =        with eigenvector    x1 = 𝜆2 =        with eigenvector    x2 =