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If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(−2)g(−2) + ƒ(0)g(0) + ƒ(1)g(1) defines an inner product in P2. Use this inner product to find (f, g), ||f|| and ||g|| for 2 f(x) = 3x² + 4x - 3 and g(x) = 3x² - 4x + 3. (f, g) ||| f || = ||g|| = = If A and B are arbitrary real m x n matrices, then the mapping = (A, B) trace(ATB) defines an inner product in Mmxn (recall that the trace of a square matrix M, denoted by trace(M), is the sum of its entries on the main diagonal). Use this inner product to find (A, B) and the norms ||A|| and || B|| for (A, B) = ☐ ||A|| = ||B || = = -3 -21 -1 -3 A = 2 -1 and B: = 3 -2 1 2 3 1

If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(−2)g(−2) + ƒ(0)g(0) + ƒ(1)g(1) defines an inner product in P2. Use this inner product to find (f, g), ||f|| and ||g|| for 2 f(x) = 3x² + 4x - 3 and g(x) = 3x² - 4x + 3. (f, g) ||| f || = ||g|| = = If A and B are arbitrary real m x n matrices, then the mapping = (A, B) trace(ATB) defines an inner product in Mmxn (recall that the trace of a square matrix M, denoted by trace(M), is the sum of its entries on the main diagonal). Use this inner product to find (A, B) and the norms ||A|| and || B|| for (A, B) = ☐ ||A|| = ||B || = = -3 -21 -1 -3 A = 2 -1 and B: = 3 -2 1 2 3 1

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section: Chapter Questions
Problem 17RQ
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If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(−2)g(−2) + ƒ(0)g(0) + ƒ(1)g(1) defines an inner product in P2. Use this inner product to find (f, g), ||f|| and ||g|| for 2 f(x) = 3x² + 4x - 3 and g(x) = 3x² - 4x + 3. (f, g) ||| f || = ||g|| = =
Transcribed Image Text:If f(x) and g(x) are arbitrary polynomials of degree at most 2, then the mapping (f,g) = f(−2)g(−2) + ƒ(0)g(0) + ƒ(1)g(1) defines an inner product in P2. Use this inner product to find (f, g), ||f|| and ||g|| for 2 f(x) = 3x² + 4x - 3 and g(x) = 3x² - 4x + 3. (f, g) ||| f || = ||g|| = =
If A and B are arbitrary real m x n matrices, then the mapping = (A, B) trace(ATB) defines an inner product in Mmxn (recall that the trace of a square matrix M, denoted by trace(M), is the sum of its entries on the main diagonal). Use this inner product to find (A, B) and the norms ||A|| and || B|| for (A, B) = ☐ ||A|| = ||B || = = -3 -21 -1 -3 A = 2 -1 and B: = 3 -2 1 2 3 1
Transcribed Image Text:If A and B are arbitrary real m x n matrices, then the mapping = (A, B) trace(ATB) defines an inner product in Mmxn (recall that the trace of a square matrix M, denoted by trace(M), is the sum of its entries on the main diagonal). Use this inner product to find (A, B) and the norms ||A|| and || B|| for (A, B) = ☐ ||A|| = ||B || = = -3 -21 -1 -3 A = 2 -1 and B: = 3 -2 1 2 3 1
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