Math 346

Homework is due every Friday evening, starting 9/5, on Gradescope

  • HW due 10/10: 3.4/21; 3.8/2, 3, 4, and the following:
    • A. Determine if the pair of vectors \((i, 2), (1, -2i)\) forms a linearly independent set.
    • B. Determine if the trio of vectors \((1+i, -1, 2i), (-1, 3-i, 1), (3i, -4i, -2+i)\) forms a linearly independent set.
  • HW due 10/3: 3.3/9; 3.4/3, 12, 15, 28 and the following:
    • A. Show that if \(proj_w(v) = u\), then for any scalar \(c\), \(proj_w(cv) = cu\). (Work with the projection formula.)
    • B. Show that if \(proj_w(v_1) = u_1\) and \(proj_w(v_2) = u_2\), then \(proj_w(v_1+v_2) = u_1+u_2\).
  • HW due 9/28: 3.3/1, 2, 10; 3.4/9, 10; and the following:
    • A. Compute the determinant of \( \begin{bmatrix} 1 & 1-i & 2i \\ i & 0 & 1-i \\ 1+2i & 1-3i & -1 \end{bmatrix} \)
    • B. True or false: if \(A\) and \(B\) are \(n \times n\) matrices, then \(\det(A+B) = \det(A) + \det(B)\). If true, prove. If false, give an example to demonstrate.
    • C. Let \( v = (1+i, -1, 2+3i), w = (2, 4-i, 3+5i)\). Compute \( 2v - w \text{ and } (1+2i)v - iw \)
  • HW due 9/19: 3.2/5–8, 16, and the following:
    • A. Solve the following system of equations: \( \begin{aligned}x+ 2y &= 3+i \\ 3x + (9+i)y &= 6+2i\end{aligned}\)
    • B. Solve the following system of equations: \( \begin{aligned} x+y+z &= i \\x - iy +2z &= 2+6i \end{aligned}\)
  • No HW due 9/12 due to exam. For practice: 2.9/13–38; 2.10/1–32
  • HW due 9/5: Do §2.4/2, 3, 11, 14; 2.5/3, 6, 10, 17, 24, 53, 57; 2.9/1, 2, 6; and the following:
    • A. As discussed in class, the function \( f(z) = \bar{z} \) acts geometrically like reflection across the x-axis. Interpret \( g(z) = -\bar{z} \) geometrically. Explain.
    • B. Interpret \(h(z) = iz\) geometrically. Explain.