Let T: R"→R" be a linear transformation, and let {v,, v2, Va) be a linearly dependent set in R". Explain why the set (T(v,), T(v,), T(v)} is linearly dependent. ... Choose the correct answer below. O A. Given that the set {v,, v2, v3} is linearly dependent, there exist c,, C2, C3, not all zero, such that c,v, +czv2 +C3V3 = 0. It follows that c,T(v,) +c,T(v,) +C3T(v3) #0. Therefore, the set T(v,), T(v,), T(v3)} is linearly dependent. O B. Given that the set {v,, v,, Va) is linearly dependent, there exist c,, C2, C3, all zero, such that c,v, +c,v, +C,V2 =0. It follows that c,T(v,) +c,T(v,) +C3T(v3) = 0. Therefore, the set T(v,), T(v,), T(v3)} is linearly dependent. O C. Given that the set {v,, v,, Va) is linearly dependent, there exist c,, C2, C3, not all zero, such that c,v, +c,v, +C,V3 #0. It follows that c,T(v,) +czT(v2) +c3T(v3) #0. Therefore, the set T(v,), T(v,), T(v3)} is linearly dependent. O D. Given that the set {v,, v2, v3} is linearly dependent, there exist c,, C2, C3, not all zero, such that c,v, +czv2 +C3V3 = 0. It follows that c,T(v,) +c,T(v,) +C3T(v3) = 0. Therefore, the set T(v,), T(v,), T(v3)} is linearly dependent.

Let T: R"→R" be a linear transformation, and let {v,, v2, Va) be a linearly dependent set in R". Explain why the set (T(v,), T(v,), T(v)} is linearly dependent. ... Choose the correct answer below. O A. Given that the set {v,, v2, v3} is linearly dependent, there exist c,, C2, C3, not all zero, such that c,v, +czv2 +C3V3 = 0. It follows that c,T(v,) +c,T(v,) +C3T(v3) #0. Therefore, the set T(v,), T(v,), T(v3)} is linearly dependent. O B. Given that the set {v,, v,, Va) is linearly dependent, there exist c,, C2, C3, all zero, such that c,v, +c,v, +C,V2 =0. It follows that c,T(v,) +c,T(v,) +C3T(v3) = 0. Therefore, the set T(v,), T(v,), T(v3)} is linearly dependent. O C. Given that the set {v,, v,, Va) is linearly dependent, there exist c,, C2, C3, not all zero, such that c,v, +c,v, +C,V3 #0. It follows that c,T(v,) +czT(v2) +c3T(v3) #0. Therefore, the set T(v,), T(v,), T(v3)} is linearly dependent. O D. Given that the set {v,, v2, v3} is linearly dependent, there exist c,, C2, C3, not all zero, such that c,v, +czv2 +C3V3 = 0. It follows that c,T(v,) +c,T(v,) +C3T(v3) = 0. Therefore, the set T(v,), T(v,), T(v3)} is linearly dependent.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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