Math Assistance

For Q2.jpg: How to i get the equation on the right side from the left?

For Q3.jpg: If i want replace all s with jw. Can i said s^4 and s^2 will have positive sign (+) and s^3 and s will have negative sign (-)?

For Q4: How to i get the matrix?

Thanks!!

Hi,

Q2: The equation on the right is the numerator of the equation on the left.

Q3: j is the sqrt(-1), so j^2 is considered to be -1, and (-1)^2 is the same as j^4 so that equals 1.

Table:
j^1= j
j^2= -1
j^3= -j
j^4= 1

and for powers over 4 repeat the same pattern:
j^5=j^1= j
j^6=j^2=-1
j^7=j^3=-j
j^8=j^4=1

etc.

and note all we did was subtract 4 from the exponent repeatedly until the exponent is 4 or less. So:

j^9=j^(9-4)=j^5=j^(5-4)=j^1=j

and also for example j^15:
j^15=j^(15-4)=j^(11)=j^(11-4)=j^(7)=j^(7-4)=j^(3)=-j

Q4:
Take the transpose of the matrix and multiply by the matrix in that exact order, then calculate the inverse matrix.

Hi MrAl,

Thanks so much! I had gotten Q3 and Q4 answer.
But for Q2, i still not able to get it. I try to multiply the equation on the left with all numerator and denominator with sTi (S + 1) and solve it, but my question doesnt get the equation on the right.

Hello again,

Well, if you multiply the left side out completely you get an equation with that right side in the numerator if you simplify it right. It might help to multiply by s^2+s too.
So i guess you could say that the equation on the right is the equation on the left multiplied by (s^2+s).