Given

a=2+3j

and

b=3-4j

, where

j=\\\\sqrt(-1)

, find (use just pencil and paper, not software or calculators)\ i.

a+b

\ ii.

a*b

\ iii.

,(a)/(b)

(Realize the denominator)\ Given

A=[[1,2],[-3,-4]],B=[[4,3],[-2,1]]

, and

c={[-2],[1]}

, find (use just pencil and paper, not software or calculators)\ )\ Solve the ordinary differential equation (ODE),

(dx)/(dt)=-2x+4,x(0)=-1

. That is, find the full solution,

x(t)

, using pencil and paper (not using software).\ Problem 1.12 in Textbook.\ 1.12 The displacement of a certain object is described by

y(t)=23sin5t

, where

t

is measured in seconds. Compute its period and its oscillation frequency in rad/sec and in hertz.\ Problem 1.14 in Textbook.\ 1.14 The displacement in meters of a certain vibrating mass is described by

x(t)=0.005sin6t

. What is the amplitude and frequency of its velocity

x^()(t)

? What is the amplitude and frequency of its acceleration

x^()(t)

?

1. Given a=2+3 jand b=34j, where j=1, find (use just pencil and paper, not software or calculators) i. a+b ii. ab iii. a/b (Realize the denominator) 2. Given A=[1324],B=[4231], and c={21}, find (use just pencil and paper, not software or calculators) \begin{aligned} i. & A+B ii. & AB iii. & Ac iv. & cTA v. & cTc vi. & \( \mathbf{c} \cdot \mathbf{c}^{T}\end{aligned} \) 3. Solve the ordinary differential equation (ODE), dtdx=2x+4,x(0)=1. That is, find the full solution, x(t), using pencil and paper (not using software). 4. Problem 1.12 in Textbook. 2 The displacement of a certain object is described by y(t)=23sin5t, where t is measured in seconds. Compute its period and its oscillation frequency in rad/sec and in hertz. 5. Problem 1.14 in Textbook. 4 The displacement in meters of a certain vibrating mass is described by x(t)=0.005sin6t. What is the amplitude and frequency of its velocity x(t) ? What is the amplitude and frequency of its acceleration x(t)