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- October 1st 2007, 08:40 PM #1

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- Sep 2006
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- 221

## Lin. Dep.

1.) Given the set with these two vectors:

I have to find the value(s) of a that makes it linearly depedent.

WORK:

Well, they are lin. dep. if they are multiples of each other. So I eye-balled it (not sure how else to do it) and saw that a = 3 will make it lin. dep because then you have the two rows are multiples of each other (scalar of 2)

__Is that the only value?__

2.) Like above..but with 1 more vector..given the set with these 3 vectors:

I have to find the value(s) of a that makes it linearly depedent.

WORK:

I can't eye-ball any a that will make these multiples of each other or will make a whole column all 0....I conclude that there is no value a for which this is linearly dependent??

- October 2nd 2007, 06:10 AM #2

- October 2nd 2007, 06:17 AM #3
Here we need to define linearly dependent a bit more carefully. If three vectors are linearly dependent we may take a linear combination of any two of them and produce a third. So one example of this is

where c and d are some constants.

So we have the equations:

I'll let you solve the system for a, c, and d.

Note: You may set up the 2 other examples, reordering the vectors as you do, and you will get the same value for a, but obviously with different values of c and d for each.

-Dan

- October 2nd 2007, 07:23 PM #4

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