22.  Which of the following statements are NOT correct?

(A) Any linear operator on an n-dimensional vector space that has fewer than n distinct eigenvalues is not diagonalizable. 

(B) Two distinct eigenvectors corresponding to the same eigenvalue are always linearly independent.

(C) If A is an eigenvalue of a linear operator T, then each vector in the eigenspace is an eigenvector of T. 

(D) A linear operator 7 on a finite-dimensional vector space is diagonalizable if and only if the multiplicity of each eigenvalue A equals the dimension of the corresponding eigenspace . 

(E) If A is diagonalizable, then   is also diagonalizable.

23.  Which of the following statements are NOT correct? (A) If S is linearly independent and generates V, each vector in V can be expressed uniquely as a linear combination of vectors in S. (B) Every vector space has at least two distinct subspaces. (C) No vector is its own additive inverse. (D) All vector spaces having a basis are fnitely generated. (E) Any two bases in a finite-dimensional vector space V have the same number of elements.

24.  Let W1 and W2 be subspaces of a finite-dimensional vector space V. Let ⊕ denote the direct sum. Which of the following statements are correct? (A) W1 ∩W2 is a subspace of V. (B) W1 ∩W2 is a subspace of V. (C) W1+W2 is a subspace of V. (D) If V = W1 ⊕W2, and β1 and B2 are bases for W1 and W2, respectively, then β1 and B2 = 0, and β1 ∪ β2 is a basis for V.  (E) If  W1 ⊕ W2 = V, then the dimension dim(V) = dim(W1)+dim(W2).

25.  Which of the following statements are correct? (A) If Q is orthogonal, then det(Q) = ±1.  (B) Let A be a real n x n matrix. Then A is symmetric if and only if A is orthogonally equivalent to a real diagonal matrix. (C) Let A ∈ be a matrix whose characteristic polynomial splits over . Then A is orthogonally equivalent to a real upper triangular matrix.  (D) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product space V. Then every eigenvalue of T is positive. (E) Let T be a self-adjoint (Hermitian) operator on a finite-dimensional inner product space V. Then every eigenvalue of T is negative.

51將生的食材或經過處理、熟製後的食材，與調味料拌勻，即可食用的菜餚，此烹調技法稱為(A)煮(B)川(C)拌(D)炒。

52利用水蒸氣的溫度，使食材熟透的一種烹調技巧稱為(A)煮(B)蒸(C)拌(D)炒。

53為使食材具有特殊香味的烹調法，以小火慢煮的方式，稱為(A)煮(B)川(C)炒(D)滷。

54三色蛋所使用的三種蛋是(A)鴨蛋、滷蛋、鹹蛋(B)雞蛋、皮蛋、鹹蛋(C)雞蛋、皮蛋、滷蛋(D)鴨蛋、雞蛋、鹹蛋。

55以發酵方法製作泡菜，其酸味是來自於醃漬時的(A)碳酸菌(B)乳酸菌(C)酵母菌(D)酒釀。

56添加相同比例量的水於糯米中，烹煮後的圓糯米比尖糯米之質地(A)較硬(B)較軟(C)較鬆散(D)相同。

57含有筋性的澱粉類(A)麵粉(B)玉米粉(C)太白粉(D)甘藷粉。

114年 - [無官方正解]114 臺灣綜合大學系統_學士班轉學生考試試題:線性代數#137898

112年 - 112 國立台灣大學_碩士班考試入學試題:線性代數(A)#130266

110年 - 110 國立政治大學_碩士暨碩士在職專班招生考試_應用數學系:線性代數#139827

110年 - 110 國立清華大學碩士班考試入學試題_數學系碩士班:線性代數#105741

110年 - 110 國立高雄大學_碩士班招生考試_應用數學系：線性代數#105691

110年 - 110 國立中央大學_碩士班招生考試_數學系/數學、應用數學組(一般生、在職生):線性代數#105306

110年 - 110 國立清華大學碩士班考試入學試題_數學系:線性代數#104957

110年 - 110 國立中山大學碩士暨碩士專班招生考試_應數系碩士班/乙組:線性代數乙#104340

110年 - 110 國立中山大學碩士暨碩士專班招生考試_通訊所碩士班/甲組:線性代數#104309

110年 - 110 國立中山大學碩士暨碩士專班招生考試_應數系碩士班/丙組:線性代數丙#104308