Answer:
The dimensions of matrix A are 2x4. option (d) is true.
Explanation:
To determine the dimensions of matrix A in the equation A × B = C, where matrix B has dimensions 4x2 and matrix C has dimensions 3x2, we can use the property of matrix multiplication.
The dimensions of the product of two matrices A and B, denoted as
A × B, is determined by the number of rows in A and the number of columns in B.
Specifically, if A is of dimension m×n and B is of dimension n×p, then the resulting product A × B will have dimensions m×p.
Given:
Matrix B has dimensions 4x2 (4 rows, 2 columns)
Matrix C has dimensions 3x2 (3 rows, 2 columns)
In the equation A × B = C, the number of columns in matrix B must match the number of rows in matrix A for the multiplication to be valid.
Since B has 2 columns, the number of rows in A must also be 2 in order for the multiplication A × B to be valid. Therefore, the dimensions of matrix A are 2x?.
To satisfy the dimensions of the product, the number of columns in A must match the number of columns in B, which is 4.
Therefore, the dimensions of matrix A are 2x4.
Thus, option (d) is true.