Find a general solution of the system = 4x1 + 2x2, x2 = — Зx1 — х2. The matrix form of the system in is х. The characteristic equation of the coefficient matrix is 4 - 2 = (4 – 1)(-1– 1) – 6 3 -1 - A = 12 – 31 – 10 = (1 + 2)(^ – 5) = 0, so we have the distinct real eigenvalues 21 = -2 and 12 = 5. For the coefficient matrix A in Eq. (12) the eigenvector equation (A – AI)v = 0 takes the form [* JD-C) :)-[{] 4 – 2 3 -1- 1 for the associated eigenvector v = [a b]°.

Question

Find a general solution of the system

Find a general solution of the system
= 4x1 + 2x2,
x2 =
— Зx1 — х2.
The matrix form of the system in is
х.
The characteristic equation of the coefficient matrix is
4 - 2
= (4 – 1)(-1– 1) – 6
3
-1 - A
= 12 – 31 – 10 = (1 + 2)(^ – 5) = 0,
so we have the distinct real eigenvalues 21 = -2 and 12 = 5.
For the coefficient matrix A in Eq. (12) the eigenvector equation (A – AI)v = 0 takes
the form
[* JD-C)
:)-[{]
4 – 2
3
-1- 1
for the associated eigenvector v =
[a b]°.
Expand
Transcribed Image Text

Find a general solution of the system = 4x1 + 2x2, x2 = — Зx1 — х2. The matrix form of the system in is х. The characteristic equation of the coefficient matrix is 4 - 2 = (4 – 1)(-1– 1) – 6 3 -1 - A = 12 – 31 – 10 = (1 + 2)(^ – 5) = 0, so we have the distinct real eigenvalues 21 = -2 and 12 = 5. For the coefficient matrix A in Eq. (12) the eigenvector equation (A – AI)v = 0 takes the form [* JD-C) :)-[{] 4 – 2 3 -1- 1 for the associated eigenvector v = [a b]°.

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