\(y1=4c1e^2t+c2e^-2t+2c3e^-2t\)

\(y2=3c1e^2t+2c2e^-2t+3c^-2t\)

\(y3=c1e^2t+x3e^-2t\)

Question

asked 2021-06-15

\(\displaystyleλ{1}=-{1}\to{\left\lbrace\begin{array}{cc} {1}&{1}\end{array}\right\rbrace},λ{2}={2}\to{\left\lbrace\begin{array}{cc} {1}&-{1}\end{array}\right\rbrace}\)

asked 2021-06-17

\(\displaystyleλ_{1}={1}\Rightarrow \left\{\left[\begin{array}{c}2\\ -1\end{array}\right]\right\},λ_{2}={3}\Rightarrow \left\{\left[\begin{array}{c}3\\ 1\end{array}\right]\right\}\)

asked 2021-01-04

The coefficient matrix for a system of linear differential equations of the form \(y^1=Ay\) has the given eigenvalues and eigenspace bases. Find the general solution for the system

\(\lambda1=3\Rightarrow \begin{bmatrix} 1 \\ 1 \\ 0 \end{bmatrix}\)

\(\lambda2=0\Rightarrow \begin{bmatrix} 1 \\ 5 \\ 1 \end{bmatrix}\begin{bmatrix}2 \\ 1 \\ 4 \end{bmatrix}\)

asked 2021-05-07

Suppose that the augmented matrix for a system of linear equations has been reduced by row operations to the given row echelon form. Solve the system by back substitution. Assume that the variables are named x1,x2,… from left to right.
[1,0,0;-3,1,0;7,4,0;1,0,1]