20F Quiz 1

# 20F Quiz 1 - = 2 r-3 s t r 4 s-2 t s 5 t t where x 2 = r x...

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

Name: PID: TA: Sec. No: Sec. Time: Math 20F Quiz 1 April 11, 2008 1. Do the vectors u = 1 4 - 3 , v = 2 2 - 1 , w = - 4 2 - 3 , span R 3 ? Why or why not? Solution: Consider the matrix A = 1 2 - 4 4 2 2 - 3 - 1 - 3 whose columns are the vectors u , v , and w . Row reduction shows that the reduced row echelon form of A is A = 1 0 2 0 1 - 3 0 0 0 . Since the last row is zero (and hence has no pivot position), it follows from Theorem 4 on page 43 of the book that u , v , and w do not span R 3 . 2. Describe the set of solutions S , in parametric form, to the homogeneous equation A x = 0 , where A = 1 - 2 0 3 0 - 1 0 0 1 - 4 0 2 0 0 0 0 1 - 5 . In other words, Fnd vectors v 1 , . . . , v k such that S = Span { v 1 , . . . , v k } . Solution: The basic variables are x 1 , x 3 , and x 5 and the free variables are x 2 , x 4 , and x 6 . The general solution is x = x 1 x 2 x 3 x 4 x 5 x 6

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.

Unformatted text preview: = 2 r-3 s + t r 4 s-2 t s 5 t t , where x 2 = r , x 4 = s , and x 6 = t . Setting r = 1 and s = t = 0, we obtain a solution v 1 = 2 1 . Similarly, v 2 = -3 4 1 corresponds to s = 1, r = t = 0, and v 3 = 1-2 5 1 corresponds to r = s = 0 and t = 1. It follows that the set of solutions to A x = is Span { v 1 , v 2 , v 3 } ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

20F Quiz 1 - = 2 r-3 s t r 4 s-2 t s 5 t t where x 2 = r x...

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

View Full Document
Ask a homework question - tutors are online