8:04 AM o 98% o Verizon webwork math ttu.edu bwork f14xiwangm2360s006 hw9 7 9: P

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8:04 AM o 98% o Verizon webwork math ttu.edu bwork f14xiwangm2360s006 hw9 7 9: Problem 7 Prev Up Next Which of the following transformations are linear? O A. T(f(t)) f(t) f' (t) from P5 to 11 O B. T (a iy) 35 iy from C to C O C. T (f(t)) f (t) 4 f(t) 3 from Coc to Coo O D. T(f(t)) f(-t) from Po to P E. T (f(t)) f (t) 2 f(t) from Coo to Coo F. T(f(t)) f (t) from P2 to P View Answers Submit Answers u have attempted this problem 6 times. ur overall recorded score is 0%. u have unlimited attempts remaining. ail instructor Page generated at 12/06/2014 at 08:04am CST WeBWork O 1996-2011 The WeBWorK Project

Explanation / Answer

A) Not linear (fails both addition and scalar multiplication).


B) This is linear.
For any x + iy, x' + iy' in C (with x, x', y, y' in R):
T(x + iy) + T(x' + iy') = (6x - iy) + (6x' - iy') = 6(x+x') - i(y+y') = T((x+x') + i(y+y'))

For any x + iy in C and scalar c in R:
c * T(x + iy) = c(6x - iy) = 6(cx) - i(cy) = T(cx, cy).

(C) E) This is linear (C? means infinitely contininuously differentiable function).

T(f(t)) + T(g(t)) = t^6 * f '(t) + t^6 * g'(t) = t^6 (f '(t) + g'(t))

E) This is linear (C? means infinitely contininuously differentiable function).

(F) This is also linear.
For any f(t), g(t) in P2 and scalar c:
T(f(t)) + T(g(t)) = t^5 * f '(t) + t^5 * g'(t) = t^6 (f '(t) + g'(t)) = T(f(t) + g(t))
and c * T(f(t)) = c* (t^5 * f '(t)) = t^5 (c f '(t)) = T(c f(t)).

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