Consider the following initial-value problem. y' + y = t sin(t), y(0) = 0 Take the Laplace transform of the differential equation and solve for L{y}. (Write your answer as a function of s.) L{y} = Use the Laplace transform to solve the given initial-value problem. Use the table of Laplace transforms as needed. y(t) =

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Q: 4. Let 0 ‡ b, c E Rn and define A = be E Rnxn. Show that (a) R(A) = span{b}, (b) N(A) = {x ≤ R" |…

A: (a) We are given that A = bcT                    where, c ∈ Rn     So, R(A) = { Ax : x ∈ Rn×1 }…