GATE Mechanical Engineering (ME) 2020 Shift 2 Solved Paper

Question : 28 of 65

Marks: +1, -0

A matrix

P

is decomposed into its symmetric part

S

and skew symmetric part

V

. If

S=(\table -4 , 4 , 2 ; 4 , 3 , 7 {/}2 ; 2 , 7{/}2 , 2 ), \;\; V=(\table 0 , -2 , 3 ; 2 , 0 , 7 {/} 2 ; -3 , -7 {/} 2 , 0 )

then matrix

P

Solution:

Matrix P is decomposed into its symmetric part S and skew symmetric part V if:-

S=[\table -4 , 4 , 2 ; 4 , 3 , 7 {/} 2 ; 2 , 7 {/} 2 , 2], V=[\table 0 , -2 , 3 ; 2 , 0 , 7 {/}2 ; -3 , -7 \/ 2 , 0]

S=\;{1}/{2}(P+P^{T})

V=\;{1}/{2}(P-P^{T})

S+V=P

P=[\table -4 , 2 , 5 ; 6 , 3 , 7 ; -1 , 0 , 2]

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