Question

How many rows and columns must a matrix A have in order to define a mapping from R⁵ into R⁷ by the rule T(x) = Ax?

Answer 1

A mapping from R⁵ to R⁷ can be defined by a matrix A with 5 rows and 7 columns, using the rule T(x) = Ax.

Step-by-step explanation:

A mapping from R⁵ (a 5-dimensional space) to R⁷ (a 7-dimensional space) can be defined by a matrix A. In order to define this mapping, the matrix A must have 5 rows and 7 columns since it represents the transformation from a 5-dimensional vector to a 7-dimensional vector. The rule for the mapping is given by: T(x) = Ax, where T(x) represents the transformed 7-dimensional vector and Ax represents the product of matrix A and the 5-dimensional vector x.