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
The Correct Option is C
Solution and Explanation
Step 1: Understand the given data
Matrix X is of order 2 × 3, meaning it has 2 rows and 3 columns.
Matrix Y is of order m × n (unknown, we have to find m and n).
The product matrix XY is of order 2 × 5.
Step 2: Condition for matrix multiplication
For two matrices X and Y to be multiplied (XY), the number of columns of X must be equal to the number of rows of Y.
Given that X has 3 columns, so m = 3.
Step 3: Determine the order of matrix Y
Since Y has order m × n, and m = 3, Y is of order 3 × n.
Step 4: Determine the number of columns n of Y
The product matrix XY has order 2 × 5, which means the number of columns of Y is 5.
So, n = 5.
Step 5: Calculate the number of elements in matrix Y
Number of elements in matrix Y = number of rows × number of columns = 3 × 5 = 15.
Final Answer: 15
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