Four matrices are given below.
`W = [(1,2),(5,8)] X = [(3,9),(7,4)] Y = [(1,3,7),(4,2,6)] Z = [(5,8),(2,9),(3,7)]`
Which of the following matix products is undefined?

Options

A. WX
B. WY
C. YZ
D. XZ

Answer

To determine which of the given matrix products is undefined, we need to analyze the dimensions of each matrix involved in the products.

1. **Identify the dimensions of each matrix:**
- Matrix \( W \) is a \( 2 \times 2 \) matrix.
- Matrix \( X \) is a \( 2 \times 2 \) matrix.
- Matrix \( Y \) is a \( 2 \times 3 \) matrix.
- Matrix \( Z \) is a \( 3 \times 2 \) matrix.

2. **Check the products one by one:**

**Option 1: \( W \times X \)**
- Dimensions: \( W \) is \( 2 \times 2 \) and \( X \) is \( 2 \times 2 \).
- For multiplication to be defined, the number of columns in \( W \) (which is 2) must equal the number of rows in \( X \) (which is also 2).
- Since \( 2 = 2 \), this product is defined.

**Option 2: \( W \times Y \)**
- Dimensions: \( W \) is \( 2 \times 2 \) and \( Y \) is \( 2 \times 3 \).
- The number of columns in \( W \) (2) equals the number of rows in \( Y \) (2).
- Since \( 2 = 2 \), this product is defined.

**Option 3: \( Y \times Z \)**
- Dimensions: \( Y \) is \( 2 \times 3 \) and \( Z \) is \( 3 \times 2 \).
- The number of columns in \( Y \) (3) equals the number of rows in \( Z \) (3).
- Since \( 3 = 3 \), this product is defined.

**Option 4: \( X \times Z \)**
- Dimensions: \( X \) is \( 2 \times 2 \) and \( Z \) is \( 3 \times 2 \).
- The number of columns in \( X \) (2) does not equal the number of rows in \( Z \) (3).
- Since \( 2 \neq 3 \), this product is undefined.

3. **Conclusion:**
- The product \( X \times Z \) is the only product that is undefined.

### Summary of the Solution:
The matrix product that is undefined is \( X \times Z \).