Find matrix X such that X =[(5,-7)(-2,3)]

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Let Y = . Then, YX = Since YX exists, we have: Number of rows of X = Number of columns in Y = 2 Number of columns of X = Number of columns in YX = 2 Order of X is 2 × 2. Let X = . Then, Solving for a and c : ∴ -2a + 3c = 7 ⇒ 2a = 3c - 7 ⇒ a = ...(1) ∴ 5a - 7c = -16 .......(2) Substituting value of a from equation (1) in (2), we get : Substituting value of c in equation (1), we get: ⇒ a = ⇒ a = ⇒ a = ⇒ a = 1. Solving for b and d: ∴ -2b + 3d = 2 ⇒ 2b = 3d - 2 ⇒ b = ....(3) ∴ 5b - 7d = -6 ......(4) Substituting value of b from equation (3) in (4), we get: Substituting value of d in equation (3), we get: ⇒ b = ⇒ b = ⇒ b = ⇒ b = -4. . Hence, X = .

Mathematics

Find matrix X such that X =[(5,-7)(-2,3)]

Matrices

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