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轉學考-線性代數
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91年 - 91 淡江大學 轉學考 線性代數#56131
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題組內容
20% 3. Let V = R
3
，and let y
1
= (1,1,0), 1/2 = (2,0,1), and y
3
= (2,2,1.) Then
(a) Find the orthonormal basis 0 of (y
1
,y
2
,y
3
).
其他申論題
(b) Find the magnetic moment of the loop? (5 %)
#213249
(a) U is onto.
#213250
(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)).
#213251
【已刪除】20% 2. Show that if W is a finite-dimensional subspace of an inner product space V. Then
#213252
(b) Find the coefficients of x = (2，1,3) in the orthonormal basis β.
#213254
(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.
#213255
【已刪除】(2) where S is a Jordan basis and J is a Jordan canonical form.
#213256
(1) Is T one-to-one?(If yes’ prove it. Otherwise, explain your answer)
#213257
(2) Is T onto?(If yes, prove it. Otherwise, explain your answer)
#213258
(1) Is T one-to-one?(If yes, prove it. Otherwise, explain your answer)
#213259
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