Let A =[(2,-1)(-3,4)] and B =[(8)(17)] . 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 × 1 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 = 1 Order of C is 2 × 1. Let C = AC = B ∴ 2x - y = 8 ⇒ y = 2x - 8 .......(1) ∴ -3x + 4y = -17 Substituting value of y from equation(1) in -3x + 4y = -17, we get: ⇒ -3x + 4(2x - 8) = -17 ⇒ -3x + 8x - 32 = -17 ⇒ 5x - 32 = -17 ⇒ 5x = -17 + 32 ⇒ 5x = 15 ⇒ x = ⇒ x = 3. Substituting value of x in equation (1), we get : ⇒ y = 2(3) - 8 ⇒ y = 6 - 8 ⇒ y = -2. Hence, C =

Mathematics

Let A =[(2,-1)(-3,4)] and B =[(8)(17)] . Find a matrix C such that AC = B.

Matrices

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