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110年 - 110 國立高雄科技大學_碩士班招生考試_電腦與通訊工程系:線性代號(甲組)#110418
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題組內容
3. [25%] Let A= (a
1
, a
2
, a
3
, a
4
) =
, where a
i
is the
column vector of Aand i = 1, 2, 3, 4.
(a) Find the rank of 4. (5%)
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(b) Find a basis for the nuli space of A. (5%)
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(c) Find the dimension of the null space of A. (5%)
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(d) Determine whether or not the column vectors a1, a2, a3 are linearly independent. Please answer independent or dependent. (5%)
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(e) Find a nonzero vector x in R3, which is orthogonal to both a1 and a 2. (5%)
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(a) Find a matrix A such that L(x) = Ax for every x = in R3.(5%)
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(b) Find the kernel of the linear transformation L (5%)
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(c) Is Lone-to-one ? Please answer Yes or No. (5%)
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(d) Is Lonto ? Please answer Yes or No. (5%)
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5. [10%] Find the least squares solution of the linear system
#472852
(a) Find the eigenspace for A corresponding to the eigenvalue 2 = 1. (5%)
#472853
相關試卷
110年 - 110 國立高雄科技大學_碩士班招生考試_電腦與通訊工程系:線性代號(甲組)#110418
110年 · #110418