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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% 1. Let V be a vector space, and suppose that T and U are linear operators on V such that
(a) U is onto.
其他申論題
(b) If someone now pulls the loop directly away from the wire, at speed v，what electromotive force is generated? In what direction does the current flow? (12 %)
#213246
(c) What if the loop is pulled to the right at speed v，instead of away? (Give the reasons for your answer.) (3 %)
#213247
(a) What is the resultant magnetic field at the center? (20 %)
#213248
(b) Find the magnetic moment of the loop? (5 %)
#213249
(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
(a) Find the orthonormal basis 0 of (y1,y2,y3).
#213253
(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
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