If A and B are of the same order then det AB det A det B Tr

If A and B are of the same order, then det (AB) = det (A) det (B) True False The sum of the eigenvalues of a matrix equals the trace of the matrix True False If lambda is an eigenvalue of A then lambda^k is an eigenvalue of A^k for any number k. True False z_1 = (x_1, y_1) = x_1 + iy_1z_2 = (x_2y_2) = x_2+ iy_2 z_1/z_2 = x_1x_2+y_1y_2/x_2^2+y_2^2 + y y_1x_2 - x_1y_2/x_2^2 + y_2^2 (z_2 notequalto 0) True False If_z_1 = r_1e^1 theta & z_2 = r_2e^I theta_2, then Argzlz2=Argz1 + Argz2. True False

Solution

15.True.

If A and B are matrices of same order then det(AB) = det(A) det(B)

16. True.

The sum of the eigen values of a matrix equals to the trace of the matrix

17. True . If is an eigen value of a matrix A then ^k is an eigen value of A^k.

18. True.

19. False . Arg(z₁ / z₂ ) = Arg(z₁) - Arg(z₂)