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suppose
does anyone know how i do this.
i know to show something is linearly independent i would do as follows:
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You have your definitions a little backwards. If you're able to find a pair (x, y) that satisfies your equation above then you've shown that they are linearly dependent. Since that's what you're asked to prove, just find that (x, y) pair and you're done.
Wrap it in bacon
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i can see that but i dont understand where i get ad-bc=0 from
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You have 2 simultaneous equations: ax + cy = 0 and bx + dy = 0. Try solving those 2 equations for x and y. Along the way you'll need to use the fact that ad - bc = 0.
Wrap it in bacon
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You won't exactly be able to "solve" for x and y, but you will be able to say:
0*y = 0 (or 0*x = 0)
Meaning that y (or x) can be any value.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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does anyone know where the ad-bc=0 comes from this is the bit thats really confusing me! i know that the vectors are linearly dependent i just dont know how to show this using ad-bc=0.
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did you try what dude say?
ax + cy = 0
bx + dy = 0 -> multiply by c/d
bcx/d + cy = 0 -> subtract from first
ax-bcx/d = 0 -> multiply by d
adx - bcx = 0 -> divide by x
ad - bc = 0
The Beginning Of All Things To End.
The End Of All Things To Come.
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Thank you for all your help I understand this now! I was clearly going about it the wrong way!
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Actually you can simplify the solution. Instead of trying to find x and y, you can look for only one variable z.
The two vectors are linearly dependent if there is a real z so (a b) +z(c d)=0 . That means a+zc=0 and b+zd=0 or a/c=b/d or ad-bc=0
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