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Linear Algebra and Its Applications (5th Edition)
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- Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are linearly dependent in the vector space C[0,1], but linearly independent in C[1,1].arrow_forwardLet S={v1,v2,v3} be a set of linearly independent vectors in R3. Find a linear transformation T from R3 into R3 such that the set {T(v1),T(v2),T(v3)} is linearly dependent.arrow_forwardWhich vector spaces are isomorphic to R6? a M2,3 b P6 c C[0,6] d M6,1 e P5 f C[3,3] g {(x1,x2,x3,0,x5,x6,x7):xiisarealnumber}arrow_forward
- Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).arrow_forwardDetermine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1) is a vector space. If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.arrow_forwardLet T be a linear transformation from R2 into R2 such that T(1,1)=(2,3) and T(0,2)=(0,8). Find T(2,4).arrow_forward
- For which values of t is each set linearly independent? a S={(t,0,0),(0,1,0),(0,0,1)} b S={(t,t,t),(t,1,0),(t,0,1)}arrow_forwardLet u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.arrow_forwardLet x = (13, −20, 15), v1 = (1, −2, 3), and v2 = (−1, 1, 1). Then the set {v1, v2} isorthogonal. It is known that x is in span{v1, v2}. Use the dot product to determine constants a and b such that x = av1 + bv2.arrow_forward
- Find a vector of matching dimension that is not in the given span. -[]} -1 span ↓ 1arrow_forwardLet fi = 1+2x+ 3x², f2 = 1+ 3x + 5æ². %3D Let g1 = 2+ 3x + 4x2, 92 = 3+ 2x + 2x2, g3 = 1+ 4x + 7x² . For which g; , i = 1, 2, 3 does (f1, f2, gi) span R2[x]? O Only g1 . O For every gi, i = 1, 2, 3. (f1, f2, 9i) spans R2 [x]. O For no i does(f1, f2, gi) span R2 [x). Only 93. O Only 92.arrow_forward[. 17. Let aj = 4 az = and b = For what -2 h value(s) of h is b in the plane spanned by aj and a,?arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
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