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 Post subject: Linear mapsPosted: Fri, 8 Oct 2010 21:20:47 UTC
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Joined: Mon, 19 Apr 2010 13:45:05 UTC
Posts: 61
Suppose that a function F: R^2 -> R^2 satisfies the conditions:

F(1, 0) = (3, 4), F(1, 1) = (7, 11), F(1, 2) = (11, 17)

Is F a linear map?

Im not sure how to do this. I know that you need to check if scalar multiplication and addition is preserved though, but I am not sure which equation to apply it to.

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 Post subject: Re: Linear mapsPosted: Sat, 9 Oct 2010 03:34:39 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6007
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
TsAmE wrote:
Suppose that a function F: R^2 -> R^2 satisfies the conditions:

F(1, 0) = (3, 4), F(1, 1) = (7, 11), F(1, 2) = (11, 17)

Is F a linear map?

Im not sure how to do this. I know that you need to check if scalar multiplication and addition is preserved though, but I am not sure which equation to apply it to.

Hint: .

Hint 2: can you conclude F is a linear map just from knowing F at 3 points?

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 Post subject: Re: Linear mapsPosted: Sat, 9 Oct 2010 07:46:32 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12103
Location: Austin, TX
outermeasure wrote:
TsAmE wrote:
Suppose that a function F: R^2 -> R^2 satisfies the conditions:

F(1, 0) = (3, 4), F(1, 1) = (7, 11), F(1, 2) = (11, 17)

Is F a linear map?

Im not sure how to do this. I know that you need to check if scalar multiplication and addition is preserved though, but I am not sure which equation to apply it to.

Hint: .

Hint 2: can you conclude F is a linear map just from knowing F at 3 points?

Ooh! I know! Pick me!

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