Let f : R" × Rn → R be defined by f(x,y) = ã³ỹ. Verify that f is a bilinear(2-linear) form on Rn. That is, verify the following equalities: (a) For vectors, ỹ Є R^ and scalars c = R, ƒ (cx, y) = cƒ (x, y) (b) For vectors, ỹ Є R^ and scalars c = R, ƒ (ã, cỹ) = cf(x, y) (c) For vectors ‚ ÿ, žЄ R³, ƒ(˜+ ž‚ÿ) = f(x, y) + ƒ(¾‚ÿ) (d) For vectors, ÿ, žЄ R^, ƒ(˜, ÿ+ z) = ƒ (ï‚ÿ) + ƒ (x, z)
Let f : R" × Rn → R be defined by f(x,y) = ã³ỹ. Verify that f is a bilinear(2-linear) form on Rn. That is, verify the following equalities: (a) For vectors, ỹ Є R^ and scalars c = R, ƒ (cx, y) = cƒ (x, y) (b) For vectors, ỹ Є R^ and scalars c = R, ƒ (ã, cỹ) = cf(x, y) (c) For vectors ‚ ÿ, žЄ R³, ƒ(˜+ ž‚ÿ) = f(x, y) + ƒ(¾‚ÿ) (d) For vectors, ÿ, žЄ R^, ƒ(˜, ÿ+ z) = ƒ (ï‚ÿ) + ƒ (x, z)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.CR: Review Exercises
Problem 13CR
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