課程名稱︰線性代數
課程性質︰電機系必修
課程教師︰劉志文
開課學院：電資工程學院
開課系所︰電機系
考試日期（年月日）︰108.10.30
考試時限（分鐘）：50
試題 :
1. (40%)Solve the following system of linear equations:
x1 + 2x2 - x3 + 2x4 + x5 = 2
-x1 - 2x2 + x3 + 2x4 + 3x5 = 6
2x1 + 4x2 - 3x3 + 2x4 = 3
-3x1 - 6x2 + 2x3 + 3x5 = 9
2. (30%)The reduced row echelon form of a matrix A is
┌1 2 0 -1┐
R = │0 0 1 1│
└0 0 0 0┘
Determine A, give that the first and third columns of A are
┌1┐ ┌2┐
a1 =│2│and a3 =│2│
└1┘ └3┘
3. (30%)In R^2, show that a rotation by 180 degree followed by a reflection
about the x-axis is a reflection about y-axis.