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  3. which of the following are linear transformations?

Which of the following are linear transformations? Choose Linear Not Linear  The function f:?3??2 defined byf([x y z]^T)=[x?y...

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Basic Math

Which of the following are linear transformations?

Choose Linear Not Linear  The function f:?3??2 definedbyf([x y z]^T)=[x?y 3y+z]^T.

Choose Linear Not Linear  The function a:??? such thata(x)=(x?1)+(x?2)^2.

Choose Linear Not Linear  The functiong:M2,2(?)?M2,2(?) defined byg(A)=2A+[1 2

3 4] Here, M2,2(?)) is the vector space of2×2matrices with real entries.

Choose Linear Not Linear  The function h:?2?? definedby h([xy])=x^2?y^2.

Answer & Explanation Solved by verified expert
3.7 Ratings (737 Votes)
The function fR3R2 is defined by f x y zT xy 3yzT Let X1 x1 y1 z1T and X2 x2 y2 z2T be 2 arbitrary elements of R3 and let k be an arbitrary scalar Then fX1X2 fx1x2y1y2z1z2T x1x2y1y2 3y13y2z1z2T x1y1 3y1z1Tx2y2 3y2z2T fX1fX2    See Answer
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