Let
Does this define a valid inner product on
Want to see the full answer?
Check out a sample textbook solutionChapter 5 Solutions
Differential Equations and Linear Algebra (4th Edition)
- 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 T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and nullity of T. (b) Find a basis for the kernel of T.arrow_forwardLet V be an inner product space. For a fixed nonzero vector v0 in V, let T:VR be the linear transformation T(v)=v,v0. Find the kernel, range, rank, and nullity of T.arrow_forward
- Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}arrow_forwardIn Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 39.arrow_forwardLet T:RnRm be the linear transformation defined by T(v)=Av, where A=[30100302]. Find the dimensions of Rn and Rm.arrow_forward
- Show that the function does not define an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3).arrow_forwardLet P, be the space of all polynomials of degree at most 3. Let TF₁ P, be the transformation T(p)-p'. (derivative of p) Is T linear? (Explain) Describe the image of T. Find a polynomial that spans the kernel of T.arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning