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轉學考-線性代數
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100年 - 100 淡江大學 轉學考 線性代數#55896
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題組內容
3.
(a) Let T : V →W be a linear transformation from vector space V to vector space W. Show that T is nonsingular (1-1) if and only if T maps a linearly independent set of vectors in F to a linearly independent set of vectors in W.
其他申論題
【已刪除】(b) Show that A is invertible if and only if I belongs to Span
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(a) Eigenvalues of T are either 0 or 1.
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【已刪除】(b) V = ker(T) range(T).
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(c) T is diagonalizable.
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(b) Let T : V→W be a, linear transformation from vector space V to vector space W. Suppose dimV = dimVK. Show that T is one to one if and only if T is onto.
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【已刪除】6. (15 points) Let A = . Determine whether A similar to a diagonal matrix over If so, exhibit a basis for such that A is similar to a diagonal matrix.
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【已刪除】7. (10 points) Let A be a, n x n matrix over the field be two distinct eigenvalues of A and W1,W2 be the corresponding eigenspaces for respectively. Show that
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【已刪除】8. (10 points) Let V be a, finite dimensional vector space over a field F and dim V≥ 2. Let T : V→ 1/ be a linear transformation. If there exists a vector v G V such that V is spanned by prove that the characteristic polynomial of T is equal to it minimal polynomial.
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⑴二級工業用水（Secondary industrial water supply）
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⑵水頭損失（Head loss）
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