Given A = ; find the matrix X such that XA = B.

Question

KnowledgeBoat · Accepted Answer

Let order of matrix X = m × n Given, XA = B Since, the product of matrices is possible only when the number of columns in the first matrix is equal to the number of rows in the second. ∴ n = 2 Also, the no. of rows of product (resulting) matrix is equal to no. of rows of first matrix. ∴ m = 1 Order of matrix X = m × n = 1 × 2. Let matrix X = Substituting matrix in XA = B we get, ∴ 3a - 2b = -2 .........(1) 6a - 8b = 16 .........(2) ⇒ 3a - 2b = -2 ⇒ 2(3a - 2b) = 2(-2) ⇒ 6a - 4b = -4 .........(3) Subtracting equation (2) from (3), we get : ⇒ 6a - 4b - (6a - 8b) = -4 - 16 ⇒ 6a - 6a - 4b + 8b = -20 ⇒ 4b = -20 ⇒ b = ⇒ b = -5. Substituting value of b in equation (1), we get : ⇒ 3a - 2(-5) = -2 ⇒ 3a + 10 = -2 ⇒ 3a = -2 - 10 ⇒ 3a = -12 ⇒ a = ⇒ a = -4. Hence, X = .

Mathematics

Given A = ; find the matrix X such that XA = B.

Matrices

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