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: