Question

Consider an n× mmatrix A, an r× smatrix B, and a vector_{$\overrightarrow{\mathbf{x}}$}in${\mathbf{ℝ}}^{\mathbf{p}}$. For which values of n, m, r,s, and pis the product$\mathbf{A}\left(B\overrightarrow{x}\right)$defined?

Short answer

The values of n, m, r, s and p is the product of $A\left(B\overrightarrow{x}\right)$is defined are s = p and m = r

Step-by-step solution

Find the solutions of the systems

For m=rto be defined the number of columns of B must be equal the number of components of$\overrightarrow{x}$.

So columns of B are [s] components of$\overrightarrow{x}$is p

For $A\left(B\overrightarrow{x}\right)$to be defined we must have m=r

Final answer:

The values of n, m, r, s and p is the product of$A\left(B\overrightarrow{x}\right)$ is defined are s = p and m = r