(b) Does 〈.，.〉 define an inner product on R³ ? Explain your answer.

(a) Find the characteristic polynomial of A.

(b) Find a Jordan form of A.

(c) Find a matrix P such that AP is the Jordan form in (b). 

(a) Fiud an orthonormal basis for W.

(b) Find the projection matrix onto W.

(c) Compute the projection of v = (1, 1,0, 1)T on W.

1.(20pt) Figure 1 is a summing op-amplifier to produce the output v0 = -10v1 -4v2+5v3 + 2v4・ The resistors R1 = 20 kΩ and R3 = 80 kΩ. The op-amplifier is ideal. Please determine the values of resistors R2, R4, R5 and R6. (5pt*4)

2.(30pt) For the circuit shown in Figure 2, the transistor parameters of Q1 and Q2 are: = 1.2 V, = 1.6 mA/V2, and neglect channel length modulation effect. Let R1 + R2 + R3 = 300 kΩ and Rs = 10 kΩ. = 5 V, -Vs =-5 V. (a) Please determine the R1, R2, R3 and RD such that DC current ID = 0.4 mA and DC voltage Coupling capacitor Cc is large enough that can be treated as short circuit for AC analysis. Please also find the voltage gain of small signal. (5pt*6)

3.(25pt) The circuit configuration to be designed is shown in Figure 3 and the = -40. Assumingβ = 100, 0.7 V, and neglect Early effect. Thermal voltage VT = 26 mV. Please find the value of = 4 V and IE = 0.2 mA. And calculate the corresponding values of the AC voltage gain input resistance . Coupling capacitor Cc is large enough that can be treated as short circuit for AC analysis. (5pt*5)

4.(25pt) For the circuit shown in Figure 4, the parameters are: = 0.1 kΩ, R1 = 40 kΩ, R2 = 5.72 kΩ, RE = 0.5 kΩ, Rc = 5 kΩ, and RL = 10 kΩ. The transistor parameters are: β = 150,  0.7 V, neglect Early effect, Cπ = 35 pF, Cμ = 4 pF, Cc= 1 μF. Thermal voltage VT = 26 mV. Please determine the lower and upper corner frequency (fL and fH), midband gain. (10pt, 10pt, 5pt)

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

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