Let\

vec(x)^(')=[[1,1,-2]]\ 0vec(x)\ x(t)=[[e^(t),e^(-2t),-3e^(-2t)]]\ 0,hat(x)(t)=[[4e^(-2t),0,0]]\ -12e^(-2t).

\ Verify that the matrix

x(t)

is a fundamental matrix of the given linear system.\ Determine a constant matrix

C

such that the given matrix

hat(x)(t)

can be represented as

hat(x)(t)=x(t)C

.\

C=[[,]] help (matrices)

\ The determinant of the matrix

C

is help (numbers)\ which is Therefore, the matrix

hat(x)(t)

is

Let x=[1012]xX(t)=[et0e2t3e2t],X^(t)=[4e2t12e2t00] Verify that the matrix X(t) is a fundamental matrix of the given linear system. Determine a constant matrix C such that the given matrix X^(t) can be represented as X^(t)=X(t)C. C=[]help(matrices) The determinant of the matrix C is help (numbers) which is Therefore, the matrix X^(t) is