1502JTest3 - . 4. (25) The matrix A = 1 1-4 4 2 2-1 1 has...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Name±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± 15 April 2004 Teaching Assistant±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Hour Test 3 Math 1502J 2pm Andrew Instructions: 1. Closed book. 2. Show your work and explain your answers and reasoning. 3. Calculators may be used, but pay particular attention to instruction 2. To receive credit, you must show your work. Unexplained answers, and answers not supported by the work you show, will not receive credit. 4. Express your answers in simplified form. 1. (25) Use the Normal Equations method to find the least squares solution to Ax = b where A = 1 1 2 0 - 1 2 ˆ ˜ ˜ ˜ and b = - 6 4 11 ˆ ˜ ˜ ˜ . 2. (25) Find a basis for the Image and a basis for the Kernel of the matrix A = 1 3 1 4 2 0 - 4 2 1 1 - 1 0 1 1 - 1 0 ˆ ˜ ˜ ˜ ˜ . 3. (25) Use the cross product to find the area of the triangle with vertices at P = 1 1 4 ˆ ˜ ˜ ˜ , Q = 1 2 6 ˆ ˜ ˜ ˜ , and R = - 1 4 2 ˆ ˜
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: . 4. (25) The matrix A = 1 1-4 4 2 2-1 1 has characteristic polynomial 1 -t ( ) 2 -t ( ) 2 . a. Find all eigenvalues and eigenvectors of A . b. Either find an invertible matrix S and a diagonal matrix D with S-1 AS = D or explain why no such S and D exist. Name Page 2 of 2 Math 1502J 2pm Andrew Hour Test 3 Teaching Assistant 15 April 2004 Answers. 1. -1 3 2. A basis for the kernel is 2-1 1 . A basis for the image consists of the pivot columns 1 2 1 1 , 3 1 1 , 4 2 3. 21 4. a. l = 1 , -1-2 1 and = 2 , 1 2 , 1 2 b. S =-1 1 1-2 2 1 2 D = 1 2 2...
View Full Document

Page1 / 2

1502JTest3 - . 4. (25) The matrix A = 1 1-4 4 2 2-1 1 has...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online