# A solution to Linear Equations

May 29th, 2015
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one of the most frequently recurring practical problems in many fields of study- such as mathematics, physics and biology

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Linear AlgebraAssignment #1Of Chapter 1Recommended Books: 1. Bernard Kolman and David Hill, Elementary Linear Algebra, Latest Edition Prentice Hall, ISBN: 0130457876. 2. Kenneth Hardy, Linear Algebra for Engineers and Scientists Using Matlab, Latest Edition, Prentice Hall, ISBN: 0139067280. 3. Stephen Goode, Differential Equations and Linear Algebra, Latest Edition, Prentice Hall, ISBN: 013263757XQ#1The director of a trust fund has \$100.000 to invest. The rules of the trust state that both a certificate of deposit (CD) and a long-term bond must be used. The director's goal is to have the trust yield \$7800 on its investments for the year. The CD chosen returns 5% per annum and the bond 9%. The director determines the amount x to invest in the CD and the amount y to invest in the bond as follows:Since the total investment is \$100,000, we must have x +y = 100.000. Since the desired return is \$7800. We obtain the equation 0.05x + 0.09y = 7800. Thus, we have the linear system Solution:x + y = 1000000.05x + 0.09y = 7800(6)To eliminate x, we add (-0.05) times the first equation to the second, obtaining (0.04)y = 2800.an equation having no x term. We have eliminated the unknown x. Then solving for y, we havey = 70.000.and substituting into the first equation of (6), we obtain x = 30.000.To check that x = 30.000, Y = 70.000 is a solution to (6), we verify that these values of x and y satisfy each of the equations in th

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