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JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Matrices

Let

A = [x 1 10], x \in R

and

A^{4} = [a_{ij}]

. If

a_{11} = 109

, then

a_{22}

is equal to ______.

Answer: 10

Solution

Squaring,

A^{2} = [x^{2} + 1 x x 1]

, and squaring again the top-left entry of

A^{4}

is

(x^{2} + 1)^{2} + x^{2}

. Setting this equal to

109

and putting

u = x^{2}

gives

u^{2} + 3 u - 108 = 0

, so

u = 9

. The bottom-right entry of

A^{4}

is

x^{2} + 1 = u + 1 = 10

.

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Integer answer

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