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Given that x11 x12 x = x21 x22 (a) Calculate Y = (X + XT) and Z = }(x − x³). (b) Show that Y is a symmetric matrix. (c) Show that Z is a skew-symmetric matrix, that is to show ZT = -Z. (d) Show that Y+Z = X. (e) Show that YT is symmetry. (f) Show that ky is symmetry where k is any scalar.

Given that x11 x12 x = x21 x22 (a) Calculate Y = (X + XT) and Z = }(x − x³). (b) Show that Y is a symmetric matrix. (c) Show that Z is a skew-symmetric matrix, that is to show ZT = -Z. (d) Show that Y+Z = X. (e) Show that YT is symmetry. (f) Show that ky is symmetry where k is any scalar.

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 64E
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Given that x11 x12 x = x21 x22 (a) Calculate Y = (X + XT) and Z = }(x − x³). (b) Show that Y is a symmetric matrix. (c) Show that Z is a skew-symmetric matrix, that is to show ZT = -Z. (d) Show that Y+Z = X. (e) Show that YT is symmetry. (f) Show that ky is symmetry where k is any scalar.
Transcribed Image Text:Given that x11 x12 x = x21 x22 (a) Calculate Y = (X + XT) and Z = }(x − x³). (b) Show that Y is a symmetric matrix. (c) Show that Z is a skew-symmetric matrix, that is to show ZT = -Z. (d) Show that Y+Z = X. (e) Show that YT is symmetry. (f) Show that ky is symmetry where k is any scalar.
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