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KCET2026MathematicsMatrices

Let X be a matrix of order 2 n and Z be a matrix of order 2 p . If n = p , then the order of the matrix 8X - 9Z is:

Options

  1. A2 n
  2. Bp 2
  3. Cn 3
  4. Dp n

Correct answer

A. 2 n

Step-by-step solution

The order of matrix X is 2 n . The order of matrix Z is 2 p . Since n = p , the order of matrix Z can be written as 2 n . Scalar multiplication does not change the order of a matrix, so the order of 8X is 2 n and the order of 9Z is 2 n . Matrix addition or subtraction is defined only for matrices of the same order, and the resulting matrix has the same order. Thus, the order of the matrix 8X - 9Z is 2 n . Answer: 2 n

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