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> 91年 - 91 淡江大學 轉學考 線性代數#56131
91年 - 91 淡江大學 轉學考 線性代數#56131
科目：
轉學考-線性代數 |
年份：
91年 |
選擇題數：
0 |
申論題數：
11
試卷資訊
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轉學考-線性代數
選擇題 (0)
申論題 (11)
(a) U is onto.
(b) The null spaces of T and U are finite-dimensionai.
Then the null space of TU is finite-dimensional, and
dim(N(TU)) = dzm(N(T)) + dim(N(V)).
【已刪除】20% 2. Show that if W is a finite-dimensional subspace of an inner product space V. Then
(a) Find the orthonormal basis 0 of (y
1
,y
2
,y
3
).
(b) Find the coefficients of x = (2，1,3) in the orthonormal basis β.
(1) Suppose that i4 is an 8 x 8 matrix, A - I has nullity 2，(A - I)
2
has nullity 4, (A- I)
k
has nullity 5 for ≥ 3, and (A + 2)
j
has nullity 3 for j ≥ 1.
【已刪除】(2)
where S is a Jordan basis and J is a Jordan canonical form.
(1) Is T one-to-one?(If yes’ prove it. Otherwise, explain your answer)
(2) Is T onto?(If yes, prove it. Otherwise, explain your answer)
(1) Is T one-to-one?(If yes, prove it. Otherwise, explain your answer)
(2) Is T onto?(If yes, prove it. Otherwise, explain your answer)
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where S is a Jordan basis and J is a Jordan canonical form.