教甄諮商輔導專業

【題組】⑶承⑵所提的做法通常會限制例如：使用者必須在三分鐘內回應輸入送至手機或是電子郵件的辨識碼。請問這樣的做法的目的為何？（5 分）

二、現今很多企業網路在與網際網路連結的閘道路由器（gateway router）使用網路位址轉換（Network Address Translation, NAT）技術，使得企業網路內部之聯網裝置的

【題組】(d) modulus of rigidity(5%), and

【題組】 (e) what would be the factor of safety with respect to slip if a one-inch diameter bar of the s

3. A hollow shaft has an outside diameter of 150 mm and an inside diameter of 60 mm. Theshaft is fix

4.Determine the maximum load P that can be applied the beam shown in Figure 4 if the allowable bendi

5,Find the forces in the members BFt and CE of the truss shown in Figure 5. (15%)

1.Let A=【題組】(a) Find a matrix V that diiigonalizes A. (10 points)

【題組】(b) Find A10. (10 points)

2.Let V be the space consistiug of all polynomials of degree less than or equal 2 and the zero polyn

【題組】(b)Find the matrix of T corresponding to the ordered bases B and D, (10 points)

3. Let A=be 3x4 matrix. (20 points)【題組】(a)Show that AX=Y is consistent for all 3x1 matrix Y.

【題組】(b)Find a basis for the solution space of AX=0.

4.Let u1= (1,1) and u2 = (1,-1)，and let T : R2 →R2 be the linear operator such thatFind a formula fo

5.【題組】(a)x -y is orthogonal to W. (10 points)

【題組】(b)||x-y||＜ ||x-z|| for all z in W that is different froin y. (10 points)

6. Let A be a nxn reai nsalrix. Prove that if A2 + l= 0, where 1 is the identity matrix，then n is ev

1.(5 points) Let A and B be n x n matrices. IsIf so, prove it; if not, give a counterexample(反例）and

2.(5 points) Let a, b and c be real numbeis(實數)such that abc ≠ 0. Prove that the plane ax + by -f- c

3.(10 points) Let T :be a linear transformatioa. If T([l,0,0]) = [-3,1], T([0，l,0]) = [4,-1], and T(

4.Let L :be a linear transibnnation defined by L【題組】(a)(5 points) Find the standard matrix represent

【題組】(b)(5 points) Sliow that L is invertible(可逆）.

【題組】(c)(5 points) Find a formula for L-1

5.(10 points) Let K be a vector space with basis(基底）

6.Given a linear system,【題組】(a)(5 points) lYansfer this system as a matrix form Ax = b and write dow

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