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b) A square nxn matrix S is called symmetric, if S' = S, and it is called anti- symmetric if S' = -S. Any square nxn matrix A can be written as the sum of a symmetric matrix S and an anti-symmetric matrix N, of the same dimensions, by setting: %D so that A = S+ N. i. Show that S is indeed symmetric (i.e. S = S'), that N is indeed antisymmetric (i.e. N' = -N) and that A = S+ N. %3D %D ii. Write the matrix A of question (1.a) as the sum of a symmetric and an antisymmetric matrix (i.e. calculate S and N).

b) A square nxn matrix S is called symmetric, if S' = S, and it is called anti- symmetric if S' = -S. Any square nxn matrix A can be written as the sum of a symmetric matrix S and an anti-symmetric matrix N, of the same dimensions, by setting: %D so that A = S+ N. i. Show that S is indeed symmetric (i.e. S = S'), that N is indeed antisymmetric (i.e. N' = -N) and that A = S+ N. %3D %D ii. Write the matrix A of question (1.a) as the sum of a symmetric and an antisymmetric matrix (i.e. calculate S and N).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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b) A square nxn matrix S is called symmetric, if S' = S, and it is called anti- symmetric if S' = -S. Any square nxn matrix A can be written as the sum of a symmetric matrix S and an anti-symmetric matrix N, of the same dimensions, by setting: %D so that A = S+ N. i. Show that S is indeed symmetric (i.e. S = S'), that N is indeed antisymmetric (i.e. N' = -N) and that A = S+ N. %3D %D ii. Write the matrix A of question (1.a) as the sum of a symmetric and an antisymmetric matrix (i.e. calculate S and N).
Transcribed Image Text:b) A square nxn matrix S is called symmetric, if S' = S, and it is called anti- symmetric if S' = -S. Any square nxn matrix A can be written as the sum of a symmetric matrix S and an anti-symmetric matrix N, of the same dimensions, by setting: %D so that A = S+ N. i. Show that S is indeed symmetric (i.e. S = S'), that N is indeed antisymmetric (i.e. N' = -N) and that A = S+ N. %3D %D ii. Write the matrix A of question (1.a) as the sum of a symmetric and an antisymmetric matrix (i.e. calculate S and N).
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