In each case given below, find : (a) the order of matrix M. (b) the matrix M. (i) (ii)

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KnowledgeBoat · Accepted Answer

(i) Let order of matrix M be a × 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. ∴ b = 2 Also, the no. of rows of product (resulting) matrix is equal to no. of rows of first matrix. ∴ a = 1 Order of matrix M = a × b = 1 × 2. Let M = . By definition of equality of matrices we get, x = 1 x + 2y = 2 ⇒ 1 + 2y = 2 ⇒ 2y = 1 ⇒ y = . ∴ M = . Hence, M = (ii) Let order of matrix M be a × b. i.e. Since product of matrix is possible, only when the number of columns in the first matrix is equal to no. of rows in second. ∴ a = 2. Also the no. of columns of product (resulting matrix) is equal to no. of columns of second matrix. ∴ b = 1. Hence, order of matrix = 2 × 1. Let M = By definition of equality of matrices we get, x + 4y = 13 ⇒ x = 13 - 4y ......(i) 2x + y = 5 ⇒ 2(13 - 4y) + y = 5 ⇒ 26 - 8y + y = 5 ⇒ -7y = -21 ⇒ y = 3. ⇒ x = 13 - 4y = 13 - 4(3) = 13 - 12 = 1. Hence,

Mathematics

In each case given below, find : (a) the order of matrix M. (b) the matrix M. (i) (ii)

Matrices

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