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Page 123

Monday, February 12, 2007

I read this meme from Dimaks. It goes like this:
⁽¹⁾ grab the nearest book and flip to page 123, ⁽²⁾ post the 6th to 8th sentences ⁽³⁾ acknowledge the book and the author ⁽⁴⁾ and then tag three persons in return.

So ola!
Here goes mine.

I have here Linear Algebra with Applications 4th edition just under my desk. hmm.. I borrowed it from the engineering library two weeks ago. But I can't remember reading it, or maybe I touched the pages a couple of times for some reference. Actually I was looking for the one that I always borrow, the one that is more "understandable" (Introductory to Linear Algebra with Applications 7th edition, Kolman, bernard & hill, David R), but I can't find the copy in the library so i end up taking this one instead.

Page 123. Printed on the upper right corner was sec 2 Subspaces, and the 6th sentence starts with Thereom 3.2.1.
So here's the exact thing:

"Theorem 3.2.1. If v₁, v₂, . . . , v_n are elements of a vector space V, then Span(v₁, v₂, . . . , v_n) is a subspace of V.

Proof. Let Beta be a scalar and let v=alpha₁v₁ + alpha₂V₂ + … + alpha_nv_n be an arbitrary element of Span(v₁, v₂, … , v_n). Since
betav = (betaalpha₁)v₁ + (betaalpha₂)v₂ + … + (betaalpha_n)v_n
it follows that betav is an element of Span(v₁, …, v_n)."

Phew. i think i just made my nose bleed. We had already tackled this topic on our class in CS 130 (Mathematical methods in computer science) but i have not remembered myself understanding it. hehe..

So that's page 123, 6th - 8th sentences of Linear Algebra with Applications 4th edition by Steven J. Leon. I don't know much about the book or the author. Hehe..

Now im tagging Louis, Gerome, and theJoketh. smiles