Problem 13. (7 points) Determine which of the following transformations are linear transformations 1. The transformation…
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Question “Problem 13. (7 points) Determine which of the following transformations are linear transformations 1. The transformation…”
Problem 13. (7 points) Determine which of the following transformations are linear transformations 1. The transformation T defined by T2, 13, 13) = (21,2,3).? 2. The transformation T defined by T (21,22) = (x1,20;22). ? 3. The transformation T defined by T(31,42) = (4.01 – 222,312) ? ” 4. The transformation T defined by T (21,12) = (2x – 3×2,41 +4,221). ? 5. The transformation T defined by T (11, 12, 13) = (0,0,0). ? Note: You can earn partial credit on this problem Type here to search
Answer
T(A4, z. y) is defined as T(49 2,3) and et. x=(2, 22, 4, 4) and y=(41, 42.3) & TR2 Now +(x+4)= (1+ Ye + 2q+42) = (2+ Yen (4+41)(*2742)) T(X), = (x13, 3), 7(n), = (.14283) T (X) + T (Y)= (21+4 xq+4206) xq+4206) xto) xgy x) x) x) x) x) x) x) & run +442 so x) + (x) x) TC4, foro xay x) xay xayay) xay) x) x) & (x) x) & (x) x) x) & (both) x) & (x) ) & (x) ) & (x) ) x) & (x) ) ). This is defined by T(Mod). = (x4,.x.x.rex (24.2) and (y.Y) ER2NOO T (14.42.2) T(x+4 4+4 (82+42.2) T(X) + T(Y)= (21+4 xq +4206) T(X) + T(T() = (41942.2) T(X) + T(Y) = (429.41.42.2) T+4 +4x0_4+4x0_4x0_4x0_4x0_4x0_4x0_4x0_4x0_4+4x0_4x0_4x0_4x0_4x0_4x0) T(x) foro xay.
. Here T is defined as T(3493),= (434-2×2.332) and y= (41.22.22.) T(Y)= (44.242, 342. +T(y) = ( 4.84 +441-232- 242,3×2+ 342)) T(+y), = T(24+41.92442) T(+y), = T(24+41.92442) ( 4. (9474) – 2.342742, 3.974) CER = (4 24+4y – 232-272 323+342) CER = (44, 242, 342) T(Y) = T(24+ 41, 92442) P C 4224-2exyy, 30% CRT(X). This +(x+4)=T(X) +T(Y) and + (6x) = CT (X) and RYE-IR2 and a Hure is a linear transformation. 4. Here, t is defined by T(2), 12) – (2224 – 34224+421931), ser x=(4), Hz, and y=(4)422) E1R2 Non-T(X)= (224-3342, Ye+4, 1921) C(1) = n(4 +41 et 2 + ) (2(a+y y ) (3 (M+ 42), 24+4 + 4, 1921) C(x+1), = n(4 +4, au, 1-349-3422,, 342-3423), 3423), 3423), 3423), 342),, 342),, 342),, ).
70+ Tey = (2×4+24 322-342 4 + Ya +8 ; P3/+1921) This is the T(x+4) and TEX (+ Tey). Hence, & is not an ar for (xy) & R2 Transformation, 5. Here T’s are defined by s O me T(4332926) = (0.0,0), ser n= (24.z. sey and s= (5424) IR 3- 7(x)= (0.0,0). Tye (0,0,0) TRAY) = T( + G + 42, 3 & 43) . TEXTY) = T(a) + Tey) gt Raye IR3 het CER Than T(ex) = T(exe, e, em FC. (0,0,0), = C TX Tary) = U+ Tey and Tex =CTON. & XYER2 and CR Therefore, t is a Linear transformativo.
Conclusion
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