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87年 - 87 淡江大學 轉學考 線性代數#56385
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題組內容
3. Let P
n
be the vector space of polynomials of degree at most n.Let T : P
3
→P
3
be the linear transformation defined by T(p(x)) =p''(x)+ p'(x)
(c) Find the matrix representation Ar of T relative to B'. (5%)
其他申論題
【已刪除】2(a)-Eind the rank of the matrix (10%)
#214169
(b) Determine whether the matrix given in (a) is invertible., (5%)
#214170
(a) Find the matrix representation A of T relative to B = {l,x,x2,x3}. ,(5%)
#214171
(b) Find the change-coordinates matrix from B to B' = {x,1 + x,x+ x2,x3}. (5%)
#214172
【已刪除】
#214174
5. Let A and B be both nx n matrices. Prove that the product AB is invertible if and only if both A and B are invertible. (10%).
#214175
,(a) Find the characteristic polynomial of A. (5%)
#214176
(b) Find the real eigenvalues and the corresponding eigenspaces of A. (10%)
#214177
(c) Determine whether the matrix A given in (a) is diagonalizable; if yes, please diagonalize it. (5%)
#214178
【已刪除】7. . Find a Jorden basis and the corresponding Jorden canonical form for A. (20%)
#214179