Let x\in\mathbb{R} and let P=[\table1,1,1;0,2,2;0,0,3],Q=[\table2,x,x;0,4,0;x,x,6] and R=PQP^{-1} Then which of the following options is/are correct? [JEE Adv 2019 P2]

det R=\det[\table2,x,x;0,4,0;x,x,5]+8,for all x\in\mathbb{R}

For x=1, there exists a unit vector \alphai^{⋀}+\betaj^{⋀}+\gammak^{⋀} for which R[\table\alpha;\beta;\gamma]=[\table0;0;0]

There exists a real number x such that PQ=QP

For x=0,if R[\table1;a;b]=6[\table1;a;b],then a+b=5

Matrices and Determinants

Section: Mathematics

Question : 20 of 56

Marks: +1, -0

Let x∈ℝ and let

P=[

],Q=[

]

and R=PQP−1 Then which of the following options is/are correct?

[JEE Adv 2019 P2]

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