Problem 1. (1 point)\ Consider the linear system\

vec(x)^(')=[[3,2],[-5,-3]]vec(x)

\ Find the eigenvalues and eigenvectors for the coefficient matrix.\

\\\\lambda _(1)=,vec(v)_(1)=,[,]{(:[ help (numbers) ]),( help (matrices) ):}

\ and\

\\\\lambda _(2)=,vec(v)_(2)=,[,]{(:[]),( help (numbers) ),( help (matrices) ):}

\ Find the real-valued solution to the initial value problem\

x_(1)^(')=3x_(1)+2x_(2),x_(1)(0)=3\ x_(2)^(')=-5x_(1)-3x_(2),x_(2)(0)=-10

\ Use

t

as the independent variable in your answers.\

x_(1)(t)= elp (formulas) \ x_(2)(t)= help (formulas)

\ Note: You can earn partial credit on this problem.

Problem 1. (1 point) Consider the linear system x=[3523]x Find the eigenvalues and eigenvectors for the coefficient matrix. 1=[v1=[1]and2=,v2=[help(numbers)help(matrices)]help(numbers)help(matrices) Find the real-valued solution to the initial value problem x1=3x1+2x2,x2=5x13x2,x1(0)=3x2(0)=10 Use t as the independent variable in your answers. x1(t)=x2(t)=(formulas) Note: You can earn partial credit on this