mythicgaming61

Question 2: algebra

Q2. Let be the 2n x 2n matrix whose (i, j)th entry is given by 

(a) Write down A_1 and A_2.

(b) Determine det () for all n 1. Justify your answer.

(c) Based on your answer to part (b), determine all values of n 1 for which is invertible. Justify your answer.

Given y'' + 10y' + 16y = f(t) ; y(0) = 1, and y'(0) = 0. Find yFand y(t) if:

a. f(t) = 50
b. f(t) = 5e^-10t
c. f(t) = sin5t
d. f(t) = (e^-t) cos10t

Thank you so much for your help!

1. y''+5y'+6y=12t+46y??+5y?+6y=12t+46
y(0)=13, y'(0)=?16y(0)=13, y?(0)=-16

2. Suppose the equation x''+169x=f(t)x??+169x=f(t) models a spring-mass system with forcing function f(t)f(t). Choose all possible forcing functions that would cause resonance in the system.

f(t)=9sin(169t)f(t)=9sin(169t)

f(t)=15cos(13t)f(t)=15cos(13t)

f(t)=2cos(169t)+15sin(169t)f(t)=2cos(169t)+15sin(169t)

f(t)=11cos(169t)f(t)=11cos(169t)

f(t)=14sin(13t)f(t)=14sin(13t)

f(t)=17cos(2t)f(t)=17cos(2t)

f(t)=10sin(2t)f(t)=10sin(2t)

f(t)=9sin(13t)?11cos(13t)

Find f.

Find f.

Describe the logistics of how these electrochemical immunosensors are used in cancer detection/ diagnosis for different types of tumorous cancers

What biomarkers are measured ?

What signals are sent?

How the immunosensor interacts with the body ? etc.