Let A =[(3,2)(-1,1)] and B =[(14,3)(2,4)] . Find a matrix C such that AC = B.

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A = and B = Given, AC = B Order of A = 2 × 2 Order of AC = Order of B = 2 × 2 Since AC exists, we have: Number of rows of C = Number of columns in A = 2 Number of columns of C = Number of columns in B = 2 Order of C is 2 × 2. Let C = AC = B Solving for a and c: ∴ -a + c = 2 ⇒ c = a + 2 ...(1) ∴ 3a + 2c = 14 ......(2) Substituting value of c from equation(1) in (2), we get : ⇒ 3a + 2(a + 2) = 14 ⇒ 3a + 2a + 4 = 14 ⇒ 5a = 14 - 4 ⇒ 5a = 10 ⇒ a = ⇒ a = 2. Substituting value of a in equation (1), we get : ⇒ c = 2 + 2 ⇒ c = 4. Solving for b and d : ∴ -b + d = 4 ⇒ d = b + 4 .......(3) ∴ 3b + 2d = 3 .......(4) Substituting value of d from equation (3) in (4), we get: ⇒ 3b + 2(b + 4) = 3 ⇒ 3b + 2b + 8 = 3 ⇒ 5b + 8 = 3 ⇒ 5b = 3 - 8 ⇒ 5b = -5 ⇒ b = ⇒ b = -1. Substituting value of b in equation (3), we get : ⇒ d = -1 + 4 ⇒ d = 3. Hence, C =

Mathematics

Let A =[(3,2)(-1,1)] and B =[(14,3)(2,4)] . Find a matrix C such that AC = B.

Matrices

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