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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.
(d) Determine whether or not the column vectors a
1
, a
2
, a
3
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%)
#472848
(b) Find the kernel of the linear transformation L (5%)
#472849
(c) Is Lone-to-one ? Please answer Yes or No. (5%)
#472850
(d) Is Lonto ? Please answer Yes or No. (5%)
#472851
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
(b)Find all eigenvalues for A(other thanλ =1)除了λ =1以外的其他特徵值。(5%)
#472854
(c) Find a nonsingular matrix X and a diagonal matrix D such that A can be factored into a product A = . (10%)
#472855
1.水中溶氧為環境水體品質重要指標之一。試解釋為何水中飽和溶氧量,當於鹽度為0 mg/L且水溫為25℃時約為8.7 mgL?(Henry's law constant= at 298.15°K;氧氣的密度為 1.429gL;氧氣在空氣中佔比的為21%)(20分)
#472856
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