F10HW-8 - F10 Homework 8 Section 4.1 4 A problem which is almost the same is posted in the Course Documents area and was briey shown in class You

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

View Full Document Right Arrow Icon
F10- Homework 8. Section 4.1. 4. A problem which is almost the same is posted in the Course Documents area and was briefly shown in class. You are actually expected to check all the 8 conditions. 6. The set of non singular matrices does not contain the O (zero) matrix which is singular. Accordingly this subset cannot be a subspace. (All subspaces contain the zero vector). Problem 11. a) Let A x 1 = b and A x 2 = b , then A ( x 1 + x 2 ) = A x 1 + A x 2 = 2 b . x 1 + x 2 is a solution of A x = b if and only if 2 b = b , that is if and only if b = 0 . Just the same, A ( c x 1 ) = cA x 1 = c b and c x 1 is a solution of A x = b if and only if c b = b . Either c = 0 or not, this is possible if and only if b = 0 . b) Since V ⊂ R n , the addition and scalar multiplication in V enjoy the properties that have been proved to hold in R n . c) For (3) to make sense, the vector 0 must be a solution. But A 0 = 0 , so 0 ∈ V only if b = 0 . d) If (3) does not hold,
Background image of page 1

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

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

This note was uploaded on 12/05/2011 for the course M 341 taught by Professor Hietmann during the Spring '08 term at University of Texas at Austin.

Page1 / 2

F10HW-8 - F10 Homework 8 Section 4.1 4 A problem which is almost the same is posted in the Course Documents area and was briey shown in class You

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