$30
Ü x1 − x2 +2x3 ê Üx1ê
1. Write vector 2x3 + x1 in the form Ax with x = x2 and A
3x3 x3
3x4 +3x2 + x1 x4
an appropriate matrix.
2. Find the matrix that represents the linear transform that reflects a two dimensional vector about y-axis and then rotate for 90 degree (counterclock wisely).
3. For each of the matrices below, specify whether it is square, rectangular, diagonal, upper-triangular or lower triangular:
Ñ1− i 0 0é
ã
,B = 3 0 0 ,C =
3 3 4i
Ñ3 0 0é
0 −3 0 .
0 0 −i