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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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題組內容
3. Let A=
be 3x4 matrix. (20 points)
(a) Show that AX=Y is consistent for all 3x1 matrix Y.
其他申論題
(a) Find a matrix V that diiigonalizes A. (10 points)
#212611
(b) Find A10. (10 points)
#212612
(a) Find tJie lcer(T). (10 points)
#212613
(b) Find the matrix of T corresponding to the ordered bases B and D, (10 points)
#212614
(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
6. Let A be a nxn reai nsalrix. Prove that if A2 + l= 0, where 1 is the identity matrix，then n is even. (10 poinis)
#212620
【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
be 3x4 matrix. (20 points)
be 3x4 matrix. (20 points)
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be 3x4 matrix. (20 points)