Question

If X, Y and XY are matrices of order 2 × 3, m × n, and 2 × 5 respectively, then the number of elements in matrix Y is:

• (A) 6
• (B) 10
• (C) 15
• (D) 35

Answer 1

The Correct Option is C

Step 1: Data Analysis
Matrix X is 2 rows by 3 columns (order 2 × 3).
Matrix Y has an unknown order, m rows by n columns (order m × n).
The resulting product matrix XY is 2 rows by 5 columns (order 2 × 5).

Step 2: Matrix Multiplication Compatibility
For XY to be possible, the number of columns in X must equal the number of rows in Y. Since X has 3 columns, Y must have 3 rows. Thus, m = 3.

Step 3: Order of Matrix Y (Partial)
Given m = 3, Matrix Y has an order of 3 × n.

Step 4: Order of Matrix Y (Complete)
The product matrix XY has an order of 2 × 5. This implies that the number of columns in Y is 5. Thus, n = 5.

Step 5: Element Count of Matrix Y
Matrix Y has an order of 3 rows × 5 columns. The total number of elements in Y is 3 * 5 = 15.

Final Answer: 15