課程名稱︰線性代數二
課程性質︰數學系大一必修
課程教師︰翁秉仁
開課學院：理學院
開課系所︰數學系
考試日期︰2010年03月26日(五)，11:20-12:10
考試時限：50分鐘
是否需發放獎勵金：是
試題 :
線性代數小考 2010/03/26
1. [40%] Diagonalize the following square matrix, or given a reason why it is
not diagonalizable.
┌ 2 0 1 ┐
│ 0 2 0 │
└ 0 0 1 ┘
2. [30%] Use diagonalization process to find square matrix A such that
A^2 - 2A = ┌ -3 -3 ┐
└ 2 2 ┘
Find two examples of such a matrix.
∞
3. [30%] {a_n}n=1 is a real sequence with the following recursive relation:
a_(n+2) = -2(a_(n+1) + a_n)
If a_0 = 0 and a_1 = 1, find a general formula to express a_n. No imaginary
unit i is allowed in your formula.
(Hint: You might need the Euler formula: e^(iθ) = cos θ+ i*sinθ.)
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