MATH 2Z03 Lecture 8: Math 2Z03 - 3.5 Variation of Parameters (Review)

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Solve this equation in matrix algebra for X explaining what you are doing at each simplification step: 3(BA + AX) = A + CT What sizes must the matrices be if A is m times n? Which matrices need to have inverses for X to have a unique solution? How does wanting a unique solution affect the sizes of each matrix? Using the following matrices, substitute them into your solution for (a) and hence find X (which should also all integers). A:= , B:= , C:= , We will be dealing with this matrix in this question: H := Check that (2 3 1) is an eigenvector of H and identify its eigenvalue. Evaluate the determinant of (H - lambda I) by means of a co-factor expansion and factories it (the polynomial should have very small coefficients). Find one other eigenvector of H (if you couldn't get another eigenvalue from (b) ask me for one).

MATH 1401 Application Project: Fall 2017 GROUP NAMES: (Maximum of 3 people to a group) Show all work that leads to your answer. Do not skip steps. The project is due by the beginning of class on December 6th. The shape of a can. In this project we will investigate the most economical shape of a cylindrical can. In 2014, the Campbell's soup company ciaimed that it produced 200 million cans of soup. Any money saved making a cylindrical can will be a tremendous savings in cost for a company Consider a cy lindrical can of volume V with radius r and height h. For now we will disregard the waste used in cutting the material for making the can. If our goal is to minimize the cost to make a can, we must minimize the surface area of a can. Task #1: Fill in the blanks. The function to be minimized is the surface area of a cylindrical can with radius r and height h, which is: s 2(Tr 2+h(2)subject to the constraint that the volume is constant, which is: We will minimize surface area as a function of radius only, so S in terms of r is: s)2(Tr2) +2(V/r)_and the comain of is: 0