Assigment 2 1 Let U (, , 4) and 1 (1, 1, 13) Show that the expression does not define an inner product on R, and list all inner product ariom that fail to hold 0,0) 4 0 412 413 1 (u, v) 400 4 1 13 43 2 Prove that it is a fixed vector in a seal innes product Space V, then the mapping by T () (1, 0) is a T VR defined linear transformation 3 Let V R have the Euclidean inner product, and let v (1, 0, 2) Compute T(ILD)) Let V P have the evalution inner Product at the points x6 1, 7 0, 2 1 and let v 1 x Compute T(x 2) 3 Do there exist scalars k and I such that the vectors P 2 kx 62, B l 5x 3x, P 1 2x 32 are mutually orthogonal with respect to the standard inner product of Pa 1 4 Find a basis for the oothogonal Complement of the subspace of R spanned by the vectors V (1, 4, 5, 2), V (2,1,3,0), V ( 1,3,2,2) M (1, 4, 5, 6, 9), V ( 3 2, 114, 1 (a) N3 ( 1,0, 1, 2, 1), V (2, 3, 5, 7, 8) 5 Let v be that if u and I are an immer product Space Show orthogonal unit vectors in V, then 11u v1l 6 to Use the Cauchy Schwarz inequality Prove that for all real values of a, b, 0, 2 (acro a Cos 0 b sino) a b 7 Let R have the Euclidean, inner product, the the Gram Schmidt process to transtorm the basis 1, 4, 43, 4) into an ortho normal basis U (0, 2, 1, 0), 4 (1, 1,0,0) Ug (1, 2, 0, 1) g Find 8 Obtain the Column vectors of 8 by the Gram Schmidt process to the applying the Column vector of A Find a R decomposition of the matrix A A 2 a R A U4 (1,0,0,1), A 3, A 3 1 decomposition of the matory 1 1 1 1 10 Determine whether the set of vector is Orthogonal and whether it is or the mormed with respect to the Euclidean inner produce in R (01), (20) ( ti), ( ti) (0,0) (0,1)

Question: Assigment-2 1. Let U = (, , 4) and 1 = (1, 1, 13). Show that the expression does not define an inner product

Assigment-2 1. Let U = (, , 4) and 1 = (1, 1, 13). Show that the expression does not define an inner product

Assigment-2 1. Let U = (, , 4) and 1 = (1, 1, 13). Show that the expression does not define an inner product on R, and list all inner product ariom that fail to hold @

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