Exam2-1010-S13-LinearAlgebra.pdf
... Exam 2, 10:10 am, March 12, 2013 [5] Let V be the vector space of all polynomials of degree 6 3 in the variable x with coefficients in R. Let W be the subspace of polynomials satisfying f(0) = f 0 (0) = 0. Find an orthogonal basis for W with respect to the inner product Z ...
... Exam 2, 10:10 am, March 12, 2013 [5] Let V be the vector space of all polynomials of degree 6 3 in the variable x with coefficients in R. Let W be the subspace of polynomials satisfying f(0) = f 0 (0) = 0. Find an orthogonal basis for W with respect to the inner product Z ...
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Chapter Two: Vector Spaces
... Show that it is a vector space. ( To save time, you need only prove axioms (d) & (j), and closure under all linear combinations of 2 vectors.) Show that any subspace of R3 must pass thru the origin, and so any subspace of R3 must involve zero in its description. Does the converse hold? Does any subs ...
... Show that it is a vector space. ( To save time, you need only prove axioms (d) & (j), and closure under all linear combinations of 2 vectors.) Show that any subspace of R3 must pass thru the origin, and so any subspace of R3 must involve zero in its description. Does the converse hold? Does any subs ...
Week 1: Configuration spaces and their many guises September 14, 2015
... by 1, which makes a mess of the signs in the axioms: • [a, b] = (−1)(|a|+1)(|b|+1) [b, a], • [a, [b, c]] = [[a, b], c] + (−1)(|a|+1)(|b|+1) [b, [a, c]], • [a, b · c] = [a, b] · c + (−1)(|a|+1)|b| b[a, c]. Define Gersti (n) to be the space of Z-linear combinations of n-ary operations of degree i on Ge ...
... by 1, which makes a mess of the signs in the axioms: • [a, b] = (−1)(|a|+1)(|b|+1) [b, a], • [a, [b, c]] = [[a, b], c] + (−1)(|a|+1)(|b|+1) [b, [a, c]], • [a, b · c] = [a, b] · c + (−1)(|a|+1)|b| b[a, c]. Define Gersti (n) to be the space of Z-linear combinations of n-ary operations of degree i on Ge ...
Homework 6, Monday, July 11
... Page 138, Ex. 17. Let x1 , . . . , xk be linearly independent vectors in Rn , and let A be a nonsingular n × n matrix. Define yi = Axi for i = 1, . . . , k. Prove that y1 , . . . , yk are linearly independent. Note first that matrix multiplication by any matrix B preserves linear combinations; that ...
... Page 138, Ex. 17. Let x1 , . . . , xk be linearly independent vectors in Rn , and let A be a nonsingular n × n matrix. Define yi = Axi for i = 1, . . . , k. Prove that y1 , . . . , yk are linearly independent. Note first that matrix multiplication by any matrix B preserves linear combinations; that ...
