olve the following initial value problems for the systems of equations using the matrix method. Find eigenvalues and eigenvectors and fix the undetermined coefficients by using technology (for example, Matlab or WolframAlpha) (a) x′ = x + 2y + 2z y′ = 2x + 7y + z z′ = 2x + y + 7z , x(0) = 9, y(0) = 1, z(0) = −1. (b) x′ = 9x − 7y − 5z y′ = −12x + 7y + 11z + 9w z′ = 24x − 17y − 19z − 9w w′ = −18x + 13y + 17z + 9w , x(0) = 2, y(0) = 0, z(0) = 1, w(0) = 1

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A:

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Rod Cutting

A naïve solution for the above-stated problem is to evaluate all of the possible combinations of different pieces of varying size to find the maximum revenue-generating combination. Although this method seems the easiest and quick to practice, it has exponential time complexity. So there is a need to figure out a better method than this.