Let A be a matrix such that A × =[(3,2)(-1,5)]=[(9)(11)](i) Write the order of A. (ii) Find A.

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KnowledgeBoat · Accepted Answer

(i) Let B = Then, AB = Order of B = 2 × 2 Order of AB = 1 × 2 Since AB exists, we have: Number of columns in A = Number of rows in B = 2 Number of rows of A = Number of rows in AB = 1 Order of A is 1 × 2. Hence, order of A is 1 × 2. (ii) Let A = . Then, Solving for a and b: ∴ 3a - b = 9 ⇒ b = 3a - 9 ....(1) ∴ 2a + 5b = -11 ...(2) Substituting value of b from equation (1) in (2), we get : ⇒ 2a + 5(3a - 9) = -11 ⇒ 2a + 15a - 45 = -11 ⇒ 17a = -11 + 45 ⇒ 17a = 34 ⇒ a = ⇒ a = 2. Substituting value of a in equation (1), we get : ⇒ b = 3(2) - 9 ⇒ b = 6 - 9 ⇒ b = -3. . Hence, A = .

Mathematics

Let A be a matrix such that A × =[(3,2)(-1,5)]=[(9)(11)](i) Write the order of A. (ii) Find A.

Matrices

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