Find solutions

Use the matrices below to perform the indicated operation: ABC. -2 0 9 1/2 3 0 1 0 1 A= 1 8 -3 8= -4 1 6 0= 0 1 1/2 4 5 8 7 -2 10 11.5. Suppose the elements of a two-dimensional vector x = [x1 x2] have the bivariate normal density p(x) = Prima(21, $2) as described in Section A.5.2 of Appendix A. a) Find the gradient Vp(x). Express your answer in simplified form using p(x). b) Find the derivative Op(x)/do1. Express your answer in simplified form using p(x).As discussed in the lecture, the complex envelope of Gaussian beam as a solution to the paraxial Helmholtz Equation is A(r) = q(z) exp - j 29(2)] q(2) = z + jzo- Then, the Gaussian wavefunction is U(r) = A(r) exp(-jkz) 1 A As we write q(z) R(z) TW2(2) Show Gaussian beam can be described as below: Wo U(r) = Ao exp -jkz - jk p2 W (2) exp Wz (2) 2 R(2) + is(=)