Homework Answers
In this question I am using matlab to solve the question.
a)
b) For rotation matrix R
inverse is equal to its transpose.So transpose of R will give its
inverse.
c)Scalar products are invarient under rotation
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In Exercises 1-14. find the matrix representations Rg and Rr and an invertible matrix C such that R CRC for the linear transjormation T of the given vector space with the indicated ordered bases B and B' derivative of p(x); B = (x', x', x, l), B' = (1, x , x1, x' + 1) 14. T: WW, where W sp(e, xe') and T is the derivative transformation; B (e, xe*), B = (2xe", 3e*
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3 around the z-axis through the angle π/3 counterclockwise. Hint:
Use the matrix for the rotation around the origin in R 2 for the
xy-plane. (b) Consider the rotation s of R 3 around the line
spanned by h 1 2 3 i through the angle π/3 counterclockwise. Find a
basis of R 3 for which the matrix [s]B,B is equal to A from (a).
(c) Give...
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I need help with 2 of the 3 exercises or with the 3
exercises.
LINEAR ALGEBRA TOPICS: Quadratic Forms and Sylvester's Theorem May 23, 2019 1.Let V be a real vector space of finite dimension and f: VR a function such that the expression F(v, w)-f(v+w)- f(v)-f(w) is bilinear. Assume further that f(λυ-λ2f(v) is satisfied for all λ E R and every vector UEV Prove that under these conditions f is in fact a quadratic form. Determine the bilinear form...
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