MAT 272 Assignment 2 - solutions

MAT 272 Assignment 2 - solutions - All values for d other...

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MAT 272 Assignment #2 - Solutions Due: September 22, 2009 1) Solve the following linear systems. Write solutions in parametric form. a. b. . c . d

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2) Let u and v both be solutions to the matrix equation A x = 0. Show that any linear combination of u and v is also a solution to the same equation. It is given that A( u )= 0 and A( v )= 0 . Let c 1 and c 2 be scalars, then A( c 1 u + c 2 v ) = A( c 1 u ) + A( c 2 v ) = c 1 A( u ) + c 2 A( v ) = c 1 0 + c 2 0 = 0 + 0 = 0 . So c 1 u + c 2 v is a solution to the equation A x = 0. 3) A box containing pennies, nickels and dimes has 13 coins with a total value of 83 cents. How many of each type of coin are in the box? Set up and solve a system of equations. Let p, d and n be the number of pennies, nickels and dimes respectively. There are two equations implied. p + n + d = 13 p + 5n + 10d = 83 The solution to the system is The only possible value for d is 6.
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Unformatted text preview: All values for d other than 4, 5, 6 and 7 yield negative answers and only 6 produces integer answers. Therefore there are 3 pennies, 4 nickels and 6 dimes. 4) Use a system of equations to find the equation of the parabola, y = ax 2 + bx + c , passing through the points (0, 2), (-3, -1) and (0.5, 0.75). There are three equations generated by plugging the three points into the quadratic. c = 2 9a 3b + c = -1 0.25a + 0.5b + c = 0.75 The solution to the system is , so is the equation of the parabola. 5) Describe the solution set of the system below as a linear combination of 3 vectors. 6) Let and . All linear combinations of u and v are solutions to some system of equations. Find that system....
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This note was uploaded on 11/08/2011 for the course MAT/FIN 272 taught by Professor Burns during the Spring '11 term at Central Connecticut State University.

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MAT 272 Assignment 2 - solutions - All values for d other...

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