Prelims Part I. A. Given the Matrices, find the following (10pts each) 3 Mat A = magic(4) , Mat B = [ 5 −10 1 8 7 6 6 20], Mat C = [ 11 11 −2 3 −11 5 4 30] 6 1. DET(BxC) 2. DET(A-C) 3. DET(B/C) 4. DET(A) Part I. B. Solve the following simultaneous equations (10pts) 10x + 15y - 13z = 65 7x-3y+8z =104 -5x+1x+5y+2z+9z = 25 5. Using Cramer’s rule. Part II. A. Determine if the function satisfy the Cauchy-Riemann equations. (10 pts each) 6. f(z) = z2 7. f(z) = cos2(z) 8. f(z) = z + Im(z) Part II. B. Find the harmonic conjugate of the following. (10 pts each) 2 2 9. 𝑒 𝑥 −𝑦 cos (2𝑥𝑦) 10. x2-y2+y Note: Show your solutions: