Matrices · Class 12 · CBSE · Science Mathematics
Find the matrix X satisfying AX = B, where A = [[2, 1], [1, 1]] and B = [[7, 4], [4, 3]].
Practice question from Matrices (Class 12 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
medium · Subjective · Q-80C20B
Find the matrix X satisfying AX = B, where A = [[2, 1], [1, 1]] and B = [[7, 4], [4, 3]].
Answer: Since A⁻¹ = [[1, −1], [−1, 2]], we have X = A⁻¹B = [[1, −1], [−1, 2]][[7, 4], [4, 3]] = [[3, 1], [1, 2]]. Therefore, X = [[3, 1], [1, 2]].
Solution
Since det(A) = 1, A is invertible and A⁻¹ = [[1, −1], [−1, 2]]. Thus X = A⁻¹B, which gives X = [[3, 1], [1, 2]].
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