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> 103年 - 103 淡江大學 轉學考 線性代數#55733
103年 - 103 淡江大學 轉學考 線性代數#55733
科目：
轉學考-線性代數 |
年份：
103年 |
選擇題數：
0 |
申論題數：
10
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轉學考-線性代數
選擇題 (0)
申論題 (10)
【已刪除】1. (10 pts) Determine if the set S = {(1,2,3), (0，1,1), (2,5,1)} forms a basis for
.
(a) Find the eigenvalues of A.
(b) Find an invertible matrix P such that P
-l
AP is diagonal.
(c) Use the result in (b) to compute A
10
.
(a) Find an orthonormal basis for IV.
(b) What is the dimension of W
⊥
(orthogonal complement of M,)? Justify your answer.
【已刪除】 (a) Find the matrix representation of T relative to the standard basis for M
2,2
(b) Determine if T is invertible.
【已刪除】5. (10 pts) Let T :
be a linear transformation. If
is a linearly dependent set in En, show that the set,
is also linearly dependent.
【已刪除】6. (10 pts) Suppose matrices A and B have the same characteristic polynomial
Is it true that A and B must be similar? Why?
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be a linear transformation. If 
is a linearly dependent set in En, show that the set, 
is also linearly dependent.