Find matrix A such that A × =[(2,3)(4,5)]

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Let B = Then, AB = Since AB exists, we have: Number of columns of A = Number of rows in B = 2 Number of rows of A = Number of rows in AB = 2 Order of A is 2 × 2 Let A = . Then, Solving for a and b: ∴ 2a + 4b = 0 ⇒ 2(a + 2b) = 0 ⇒ a + 2b = 0 ⇒ a = -2b ......(1) ∴ 3a + 5b = -4 Substituting value of a from equation(1) in 3a + 5b = -4, we get: ⇒ 3(-2b) + 5b = -4 ⇒ -6b + 5b = -4 ⇒ -b = -4 ⇒ b = 4. Substituting value of b in equation 1, we get, ⇒ a = -2(4) ⇒ a = -8. Solving for c and d: ∴ 2c + 4d = 10 ⇒ 2(c + 2d) = 10 ⇒ c + 2d = 5 ⇒ c = 5 - 2d .......(2) ∴ 3c + 5d = 3 Substituting value of c from equation (2) in 3c + 5d = 3, we get : ⇒ 3c + 5d = 3 ⇒ 3(5 - 2d) + 5d = 3 ⇒ 15 - 6d + 5d = 3 ⇒ 15 - d = 3 ⇒ d = 15 - 3 ⇒ d = 12. Substituting value of d in equation (2), we get, ⇒ c = 5 - 2(12) ⇒ c = 5 - 24 ⇒ c = -19. . Hence, A = .

Mathematics

Find matrix A such that A × =[(2,3)(4,5)]

Matrices

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