(1) let t: rn--->rm be linear tranformations. a. if t maps rnonto rm, give a relationship between m and n b. if t is one-to-one, give a relationship between m and n c. if t maps rn onto rm and is one-to-one, give a relationship between m and n (hint: think about the size of the standard matrix representation of t and the placement of the pivots in each case) (2) let t: r3 ---> r4 be a linear transformation such that the only solution to t(x) = 0 is trivial solution. a. if t is one-to-one b. does t map r3onto r4? justify your answers in each case. (hint:one way to approach this is to look at what the martix representation of t might look like and where it does or does not have pivots.) (3) suppose a linear transformation t: r2> r2 is formed by taking a rotation counterclockwise of 90 degrees, follwed by a reflection through the x2-axis. describe the points that will be moved back to their original position by this transformation? (hint: think about what t will do to the unit box and the vectors e1 and e2)
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Category: computerinformation | Author: Hedda Galya
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