Which of the following matrix products is undefined

Four matrices are given below.

Which of the following matrix products is undefined?

  1. WX
  2. WY
  3. YZ
  4. XW
  5. XZ

Answer

The correct answer is E.

The dimensions of a matrix can be written as (r × c), where r is the number of rows of the matrix and c is the number of columns of the matrix. To find the element in the ith row and the jth column of the product of two matrices, you must multiply the elements of the ith row of the matrix on the left with the corresponding elements in the jth column of the matrix on the right and then add those products together.

For this reason, in order for the matrix product AB to be defined, the number of columns of matrix A must be equal to the number of rows of matrix B.

The product of an (r × c) matrix (on the left) and an (m × n) matrix (on the right) is defined if and only if c = m.

The dimensions of W and X are (2 × 2), the dimensions of Y are (2 × 3), and the dimensions of Z are (3 × 2). Because X is a (2 × 2)-matrix and Z is a (3 × 2)-matrix, the matrix product XZ is undefined.