This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 3E Exam #1 Sample Laney College, Fall 2006 Fred Bourgoin 1. Consider the following system of equations. y + 2 kz = 0 x + 2 y + 6 z = 2 kx + 2 z = 1 For what values of k does the system have no solutions, exactly one solution, and infinitely many solutions? Explain your answers. 2. Circle the matrix (or matrices) in reduced row echelon form. A = 1 1 0 1 0 0 1 0 0 0 0 2 , B = 1 0 0 0 0 1 0 1 0 0 1 2 0 0 0 0 , C = 1 2 0 0 0 0 0 0 0 0 1 0 , D = 1 2 0 0 0 0 1 0 0 0 0 1 3. Compute the products. (a) 1 1 1 5 1 1 1 5 3 1 2 3 (b) 1 1 1 1 1 1 2 1 2 3 3 2 1 2 1 3 4. Determine whether each of the given types of geometric transformations in R 2 is invertible. Briefly justify your answers. (a) Rotation (b) Reflection (c) Projection 1 5. Let x = [ 1 2 ] and y = [ 1 2 ] be vectors in R 2 . For each matrix below, identify the type of geometric transformation it represents (be precise!), and determine the images of x and y . (a) [ 1 1 ] (b) [ . 8 . 6 . 6 . 8 ] (c) [ . 5 0 . 5 . 5 0 . 5 ] 6. What is the rank of the matrix A = 1 2 0 2 3 0 0 1 3 2 0 0 1 4 1 0 0 0 0 1 ? 7. Find a diagonal matrix D such that D 5 3 9 = 2 1 . 8. Find the inverse of A = 2 5 0 0 1 3 0 0 0 0 1 2 0 0 2 5 . 9. If A is an invertible matrix and c is a nonzero scalar, is the matrix cA invertible? If so, what is the relationship between A 1 and ( cA ) 1 ? 10. The momentum P of a system of 2 particles in space with masses m 1 and m 2 , and velocities v 1 and v 2 is defined as P = m 1 v 1 + m 2 v 2 . Consider two elementary particles with velocities v 1 = 1 1 1 a nd v 2 = 4 7 10 . The particles collide. After the collision, their respective velocities are observed to be w 1 = 4 7 4 a nd w 2 = 2 3 8 ....
View
Full
Document
This note was uploaded on 04/19/2011 for the course MTH 203 taught by Professor Staff during the Spring '08 term at Grand Valley State University.
 Spring '08
 Staff
 Equations

Click to edit the document details