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LS.6 Solution Matrices - MIT Mathematics

Solution MatricesIn the literature, solutions to linear systems often are expressed using square matricesrather than vectors. You need to get used to the before, we state thedefinitions and results for a 2 2 system, but they generalize immediately ton Fundamental return to the system(1)x =A(t)x,with the general Solution (2)x=c1x1(t) +c2x2(t),wherex1andx2are two independent solutions to (1), andc1andc2are arbitrary form the matrix whose columns are the solutionsx1andx2:(3)X(t) = (x1x2) =(x1x2y1y2).Since the solutions are linearly independent, we called them in afundamentalset ofsolutions, and therefore we call the matrix in (3) afundamental matrixfor the system (1).

LS.6 Solution Matrices In the literature, solutions to linear systems often are expressed using square matrices rather than vectors. You need to get used to the terminology. As before, we state the definitions and results for a 2×2 system, but they generalize immediately to n×n systems. 1. Fundamental matrices. We return to the system (1) x ...

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