Question: Work Sheet Assignment 18: Let o > 0 be a real constant and b E C([0, +00)). Consider ODES (2) - ( )()+(,0) t >

Work Sheet Assignment 18: Let o > 0 be a real constant and b E C([0, +00)). Consider ODES (2) - ( )()+(,0) t > to = 0. (a) Calculate the unit fundamental matrix (t) = eAt and check the value of its Wronskian. Simplify the matrix exponential to one matrix and show all major steps in detail. (b) Work out and simplify the (LSP) and (VOP) formulas of section 5.2 for this IVP problem (i.e. apply formulas for xy and xp as in REM 5.6 (3) in ODELec34), started at to = 0. Multiply out all related matrix-matrix and matrix-vector products! Provide all mathematical details step by step (not just final answers and not just verbal argu- ments mostly). Work Sheet Assignment 18: Let o > 0 be a real constant and b E C([0, +00)). Consider ODES (2) - ( )()+(,0) t > to = 0. (a) Calculate the unit fundamental matrix (t) = eAt and check the value of its Wronskian. Simplify the matrix exponential to one matrix and show all major steps in detail. (b) Work out and simplify the (LSP) and (VOP) formulas of section 5.2 for this IVP problem (i.e. apply formulas for xy and xp as in REM 5.6 (3) in ODELec34), started at to = 0. Multiply out all related matrix-matrix and matrix-vector products! Provide all mathematical details step by step (not just final answers and not just verbal argu- ments mostly)
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