Classifying a Point In Exercises 19-22, a
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CALCULUS EARLY TRANSCENDENTAL FUNCTIONS
- Vector Operations In Exercises 19-24, let u=(1,2,3), v=(2,2,-1), and w=(4,0,-4). Find 2u+4vw.arrow_forwardLet v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.arrow_forwardProofProve in full detail that M2,2, with the standard operations, is a vector space.arrow_forward
- Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. a Explain what it means to say that a set of vectors is linearly independent. b Determine whether the set S is linearly dependent or independent. S={(1,0,1,0),(0,3,0,1),(1,1,2,2),(3,4,1,2)}arrow_forwardRepresenting a Vector In Exercises 3-6, use a directed line segment to represent the vector. u=(2,4)arrow_forwardCalculus In Exercises 43-46, let f and g be functions in the vector space C[a,b] with inner product f,g=abf(x)g(x)dx. Let f(x)=x and g(x)=x3 be vectors in C[0,1]. aFind f,g. bFind g. cFind d(f,g). dOrthonormalize the set B={f,g}.arrow_forward
- Proof Complete the proof of the cancellation property of vector addition by justifying each step. Prove that if u, v, and w are vectors in a vector space V such that u+w=v+w, then u=v. u+w=v+wu+w+(w)=v+w+(w)a._u+(w+(w))=v+(w+(w))b._u+0=v+0c._ u=vd.arrow_forwardCalculus In Exercises 43-46, let f and g be functions in the vector space C[a,b] with inner product f,g=abf(x)g(x)dx. Let f(x)=x+2 and g(x)=15x8 be vectors in C[0,1]. aFind f,g. bFind 4f,g. cFind f. dOrthonormalize the set B={f,g}.arrow_forwardVector Operations In Exercises 11-16, find the vector v and illustrate the specified vector operations geometrically, where u=(-2,3) and w=(-3,-2). v=u+warrow_forward
- Calculus Let B={1,x,ex,xex} be a basis for a subspace W of the space of continuous functions, and let Dx be the differential operator on W. Find the matrix for Dx relative to the basis B.arrow_forwardFinding a VectorIn Exercises 13-16, find the vector v with the given length and the same direction as u. v=3,u=(0,2,1,1)arrow_forward
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