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Let A = x 1 1 0 , x ε R and A 4 = a i j . If a 11 = 109 , then a 22 is equal to_____________.

Correct answer

0

Step-by-step solution

A 2 = x 1 1 0 × x 1 1 0 = x 2 + 1 x x 1 A 4 = x 2 + 1 x x 1 × x 2 + 1 x x 1 = x 4 + 3 x 2 + 1 x 3 + 2 x x 3 + 2 x x 2 + 1 Given a 11 = 109 ⇒ x 4 + 3 x 2 + 1 = 109 x 2 + 12 x 2 - 9 = 0 ⇒ x 2 = 9 ∴ a 22 = x 2 + 1 = 10

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