True or false?

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TheWrathOfMath

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If {x1, y1, z1} and {x2, y2, z2} linearly independent in R^3, then {x1, y1} and {x2, y2} is linearly independent in R^2.

I know that the opposite claim is true, but what about this one?
 
not expert in linear algebra but say vectors are {x1, y1, z1} && {x1, y1, z2} where z2 not equal z1.
so {x1, y1, z1} is not a multiple of {x1, y1, z2} so they are linearly independent. but {x1, y1} and {x1, y1} from both vectors are linearly dependent so it is not necessary. This is the answer to my knowledge of linear independence, sorry if I am wrong but I dont know much
 
TheWrathOfMath said:
If {x1, y1, z1} and {x2, y2, z2} linearly independent in R^3, then {x1, y1} and {x2, y2} is linearly independent in R^2.

I know that the opposite claim is true, but what about this one?
Click to expand...
(0,1,0) and (0,1,1) are linearly independent, but (0,1) and (0,1) are not.
 
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