Let E and M be 3 3 matrices satisfying the system of equations aligned & E M^T=(E M)^T=20 I & (E+M)^T=17(E-M)^T aligned and where I denotes identity matrix of order 3 . If E^2+M^2= a b I (where a and b are co-prime), then find the value of

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Let E and M be 3 3 matrices satisfying the system of equations aligned & E M^T=(E M)^T=20 I & (E+M)^T=17(E-M)^T aligned and where I denotes identity matrix of order 3 . If E^2+M^2= a b I (where a and b are co-prime), then find the value of (a+b)

Quantrex Academy · Accepted Answer

Correct answer: 743

(E M)^T=20 I Take transpose on both sides E M=20 I ...(1) aligned (E+M)^T & =17(E-M)^T E^T+M^T & =17 (E^T-M^T ) 16 E^T & =18 M^T aligned Take transpose on both sides 16 E=18 M ...(2) From Eqns. (1) and (2), we get aligned E & = 3 10 2 I ; M= 4 10 3 I E^2+M^2 & = 725 18 I a+b=743 aligned

Let E and M be 3 3 matrices satisfying the system of equations aligned & E M^T=(E M)^T=20 I & (E+M)^T=17(E-M)^T aligned and where I denotes identity matrix of order 3 . If E^2+M^2= a b I (where a and b are co-prime), then find the value of (a+b)

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