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Suppose T:R3-R3 is the transformation given below. Determine whether I is one-to-one and/or onto. If it...

Suppose T:R3-R3 is the transformation given below. Determine whether I is one-to-one and/or onto. If it is not one-to-one, sh

Suppose T:R3-R3 is the transformation given below. Determine whether I is one-to-one and/or onto. If it is not one-to-one, show this by providing two vectors that have the same image under T. If T is not onto, show this by providing a vector in R3 that is not in the range of T. хо 3x0-3x4–3x2 3x0-3x1 x2 X0-X1-3x2 TX1 = T is not one-to-one: 0 0 0 0 TO = and TO 0 0 0 0 T is not onto: T is onto T is not onto: IS TIL Le image of any x under T. 0 U
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T: R3IR² is giress by T ng 30-394-3% 3xo-324 neorry-axz Let [2] Си-ex T Then T [6] - L 08. 3a3bber 3a 3b a-b-3c ca 91 39-30-3Therefore two elements of [8] and [6] have same image under T. By Rank- Nurity theorem Rank (T) + Nucity (t) = 3. or, RCT) =

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