{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MAT 272 Assignment 2 - solutions

MAT 272 Assignment 2 - solutions - The only possible value...

This preview shows pages 1–3. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The only possible value for d is 6. 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....
View Full Document

{[ snackBarMessage ]}

Page1 / 3

MAT 272 Assignment 2 - solutions - The only possible value...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online