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轉學考-線性代數
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95年 - 95 淡江大學 轉學考 線性代數#56041
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6. Let A be a nxn reai nsalrix. Prove that if A
2
+ l= 0, where 1 is the identity matrix，then n is even. (10 poinis)
其他申論題
(b) Find a basis for the solution space of AX=0.
#212616
【已刪除】4. Let u1= (1,1) and u2 = (1,-1)，and let T : R2 →R2 be the linear operator such that Find a formula for T(x, y). (10 points)
#212617
(a) x -y is orthogonal to W. (10 points)
#212618
(b) ||x-y||＜ ||x-z|| for all z in W that is different froin y. (10 points)
#212619
【已刪除】1. (5 points) Let A and B be n x n matrices. Is If so, prove it; if not, give a counterexample(反例）and state ujicler what conditions the equation is true.
#212621
【已刪除】2. (5 points) Let a, b and c be real numbeis(實數)such that abc ≠ 0. Prove that the plane ax + by -f- cz = 0 is a subspace(子空間)of
#212622
【已刪除】3. (10 points) Let T : be a linear transformatioa. If T([l,0,0]) = [-3,1], T([0，l,0]) = [4,-1], and T([0,-i, 1]) = [3,5], find T[-1,4,2]).
#212623
(a) (5 points) Find the standard matrix representation(標準矩陣表示式)of L.
#212624
(b) (5 points) Sliow that L is invertible(可逆）.
#212625
(c) (5 points) Find a formula for L-1
#212626
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