Please show the work so I learn Determine the coefficients p, q, and the determi
ID: 1813374 • Letter: P
Question
Please show the work so I learn
Determine the coefficients p, q, and the determinant (delta) of the system:
y1'=y1 + 10y2
Y'2=7y1 - 8y2
Based on these values, what is the type and stability of the critical point?
a.) p=-9, q=9, delta =16, Stable and Node
b.) p=0,q=78, delta =361, Stable and Saddle point
c.) p=-7,q, q= -78, delta = 361, Unstable and node
d.) p=10, q=9, delta =64, Stable and Saddle point
e.) None of the above; see Problem Work
Explanation / Answer
matrix A =
[1 10]
[7 -8]
|y*I - A| = 0
==>
|y-1 -10|
|-7 y+8| = 0
==>
(y-1)(y+8) - 70 = 0
==>
y^2 + 7y - 78 = 0
==>
y = 6, -13
Real, opposite sign: saddle point (unstable)
e.) None of the above;