If B = find the matrix A such that AB = C.

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KnowledgeBoat · Accepted Answer

Given, AB = C We know that matrix A will be of order 2 × 2. Let matrix be By definition of equality of matrices we get, -4a + 5b = 17 (...Eq 1) 2a - b = -1 ⇒ b = 2a + 1 (...Eq 2) -4c + 5d = 47 (...Eq 3) 2c - d = -13 ⇒ d = 2c + 13 (...Eq 4) Putting value of b from Eq 2 in Eq 1 ⇒ -4a + 5b = 17 ⇒ -4a + 5(2a + 1) = 17 ⇒ -4a + 10a + 5 = 17 ⇒ 6a + 5 = 17 ⇒ 6a = 12 ⇒ a = 2. ∴ a = 2, b = 2a + 1 = 2(2) + 1 = 5. Putting value of d from Eq 4 in Eq 3 ⇒ -4c + 5d = 47 ⇒ -4c + 5(2c + 13) = 47 ⇒ -4c + 10c + 65 = 47 ⇒ 6c + 65 = 47 ⇒ 6c = -18 ⇒ c = -3. ∴ c = -3, d = 2c + 13 = 2(-3) + 13 = 7. Since, Hence, the matrix A = .

Mathematics

If B = find the matrix A such that AB = C.

Matrices

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