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JEE Main 2022 Mathematics question

MathematicsMatricesJEE Main 2022

Let A be a real matrix such that A(1, 1, 0)ᵀ = (1, 1, 0)ᵀ, A(1, 0, 1)ᵀ = (−1, 0, 1)ᵀ and A(0, 0, 1)ᵀ = (1, 1, 2)ᵀ. If , , ᵀ and I is an identity matrix of order 3, then the system (A − 2I)X = (4, 1, 1)ᵀ has :

Answer: (2)

Solution

Writing A = and using the three given relations gives a = −2, b = 3, c = 1, d = −1, e = 2, f = 1, g = −1, h = 1, i = 2. So A − 2I = $Missing \end{bmatrix}\begin{bmatrix} -4 & 3 & 1 -1 & 0 & 1

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Question ID VK-024988