课程名称︰工程数学－线性代数
课程性质︰电机系必修
课程教师︰刘志文
开课学院：电资学院
开课系所︰电机系
考试日期（年月日）︰108.12.24
考试时限（分钟）：50
试题 :
┌-1 0 0┐
1. A = │ 0 1 2│
└ 0 2 1┘
(a)(15%) Show that the matrix is diagonalizable.
(b)(15%) Find an orthogonal matrix Q and a diagonal matrix D s.t. A = QDQ^-1.
(c)(10%) Find Q^-1.
2. Let W = Span{u1, u2}, where
┌ 1┐ ┌ 3┐
u1 =│-1│and u2 =│-3│.
│-1│ │ 1│
└ 1┘ └-1┘
(a)(15%) Find an orthonormal basis for W.
(b)(15%) Find an orthonormal basis for W perp(orthogonal complement of W).
(c)(15%) Find the orthogonal projection matrix P_{w perp}.
(d)(15%) Show that P_{w pere} + Pw = I4, where I4 is the 4x4 identity matrix.