{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

oldprelim

# oldprelim - Prelim 1 Math 294 4 questions total 100 points...

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

Prelim 1 Math 294 September 28, 2006 4 questions; total 100 points . You may use anything that has been given in class or in the book, as long as you show clearly what you are using . Calculators are neither needed nor permitted. Some pieces of formulas and definitions can be found on the bottom of the second side. 1. We are given a system of 4 linear equations in 6 unknowns in the form A x = b , and told that the augmented matrix A b row reduces to 1 3 0 -1 1 0 1 0 0 1 1 2 0 2 0 0 0 0 0 1 3 0 0 0 0 0 0 0 (a) (10 points) Find all solutions to A x = b . (b) (4 points) Let T : R p R q be the linear transformation given by T ( x ) = A x . Determine p and q . (c) (4 points) Determine rank( A ) and the dimension of image( T ). (d) (4 points) Is it true that b is an element of image( T )? Why or why not? (e) (4 points) Determine the dimension and a basis for the kernel of T . (f) (4 points) If A = v 1 | v 2 | · · · | v 6 , give a basis for image( T ). Do you have enough information to compute these vectors explicitly?

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

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

{[ snackBarMessage ]}