Final answer:
The product of matrices A2×3 and B3×4 is defined and the dimensions of the product matrix AB are 2×4.
Step-by-step explanation:
The question is asking whether the product of matrices A₂×₃ (with dimensions 2×3) and B₃×₄ (with dimensions 3×4) is defined, and if so, what the dimensions of the resulting matrix AB are.
In matrix multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix for the product to be defined. Here, matrix A has 3 columns and matrix B has 3 rows, so the product AB is defined.
The dimensions of the product matrix AB will have the same number of rows as the first matrix and the same number of columns as the second matrix. Therefore, the dimension of the product matrix AB is 2×4.