We outline an instructional task to promote the understanding of matrix-vector multiplication, and analyze how first year undergraduate mathematics students construct meanings for this product. The conceptual framework that supports this research was based on three theoretical constructs: (i) problem solving, (ii) learning with understanding, and (iii) instructional tasks. We identify that students can give meaning to the way matrix-vector product is defined,  through the relations established in the task context. Particularly, most of the students assigned meaning to the arithmetic operations (multiplications and additions) involved in the Ax product, but had difficulties to extend those meanings for understanding the matrix product AB.

understanding, matrix-vector multiplication, problem solving, instructional tasks.