20F Quiz 1

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

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

View Full Document Right Arrow Icon
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
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: = 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

Page1 / 2

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

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