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- Solved Let T ( [v1v2v3])= [v1-v10v2-v3]. a. Give a nontrivial - Chegg
Give a nontrivial vector in the range of T b Give a nontrivial vector in the kernel of T c Give the standard matrix for T Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on Question: Let T ( [v1v2v3])= [v1-v10v2-v3] a
- The Kernel and the Range of a Linear Transformation
The kernel of a linear transformation from a vector space V to a vector space W is a subspace of V Proof Suppose that u and v are vectors in the kernel of L Then L (u) = L (v) = 0 We have L (u + v) = L (u) + (v) = 0 + 0 = 0 and L (c u) = cL (u) = c 0 = 0 Hence u + v and c u are in the kernel of L We can conclude that the kernel of L is a
- Unit 3, Section 3: Null Space and Range Null Space and Range
prove the theorem in detail, as it is quite straightforward Indeed, the standard procedure applies immediately here: one must show that, if v, w 2 null (T ), then v + w 2 null (T ) as well (i e , show that T (v + w) = 0 if T (v) = 0 and T (w) = 0), and hat v 2 null (T ) (i e , show that T ( v) = 0 if T (v) = 0) Both tasks are easily a
- Show that $T(\\mathbf x)=\\mathbf 0$ has a nontrivial solution
That is, the vector x =c1u +c2v x = c 1 u + c 2 v satisfies T(x) =0 T (x) = 0 Furthermore, x x cannot be the zero vector, since that would mean that a nontrivial linear combination of u u and v v is zero, which is impossible because u u and v v are linearly independent
- S13_342_book_pgs19-20. dvi - Oregon Institute of Technology
The range of T is all polynomials of the form ax2 + (b + c)x + (a + b + c) If we let b + c = d, this is then the polynomials of the form ax2 + dx + (a + d) = a(x2 + 1) + d(x + 1)
- 1. Math 113 Homework 3 Solutions
dim range T = dim null SranT + dim range SranT Lemma 1 tells us that range SranT = range ST, and Lemma 2 tells us that null SranT = range T \ null S Substituting these, we obtain the desired equation
- -VI 6) Let T E a. Give a nontrivial vector in the range of T- b. . . .
-VI 6) Let T E a Give a nontrivial vector in the range of T- b Answered step-by-step Solved by verified expert University of Washington • MATH • MATH - 208
- Solved Math 240Problem Set | Chegg. com
a Evaluate T ([1 5]) b How do we now know that [1 5 0 2] is not in the kernel of T ? c Give an example nontrivial vector that is in the kernel of T
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