Question: Making New Bases from Old: In Problems 1-3, a vector space and a basis will be given. Construct a different basis from the given basis.

Making New Bases from Old: In Problems 1-3, a vector space and a basis will be given. Construct a different basis from the given basis. Make them substantially different, so that at least two vectors are not multiples of vectors in the original basis?
1. {iÌ…, jÌ…, kÌ…} in R3
2.

in D, the space of all diagonal matrices,
3. [sin t, cos t] in [y ( Cn(R) | yn - y = 0]

1 01 [0 0 001-10 1

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