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Matrices and Determinants

Section: Mathematics

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Question : 20

Total: 56

Let x∈ℝ and let

1	1	1
0	2	2
0	0	3

2	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[
2 x x
0 4 0
x x 5
]+8,for
all x∈ℝ
For x=1, there exists a unit vector α
⋀
i
+β
⋀
j
+γ
⋀
k
for which R[
α
β
γ
]=[
0
0
0
]
There exists a real number x such that PQ=QP
For x=0,if R[
1
a
b
]=6[
1
a
b
],then a+b=5

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