Let P_1=I=[\table 1,0,0;0,1,0;0,0,1],P_2[\table 1,0,0;0,0,1;0,1,0],P_3=[\table 0,1,0;1,0,0;0,0,1] P_4=[\table0,1,0;0,0,1;1,0,0],P_5=[\table 0,0,1;1,0,0;0,1,0],P_6=[\table0,0,1;0,1,0;1,0,0] and X=\sum^{6}_{k=1}P_k[\table2,1,3;1,0,2;3,2,1]P_k^T where P^T_k denotes the transpose of the matrix P_k.Then which of the following options is/ are correct? [JEE Adv 2019 P2]

The sum of diagonal entries of X is 18

X – 30I is an invertible matrix

If X[\table1;1;1]=\alpha[\table1;1;1],then\alpha=30

Matrices and Determinants

Section: Mathematics

Question : 19 of 56

Marks: +1, -0

Let

P1=I=[

],P2[

],P3=[

]
P4=[

],P5=[

],P6=[

]

and X=

∑

k=1

Pk[

]PkT
where PkT denotes the transpose of the matrix Pk.Then which of the following options is/ are correct?

[JEE Adv 2019 P2]

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