• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

Suggested languages for you:

Americas

Europe

Q51E

Expert-verified
Found in: Page 37

### Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

# Consider an n × m matrix A, an r × s matrix B, and a vector $\stackrel{\mathbf{\to }}{\mathbf{x}}$ in${{\mathbf{ℝ}}}^{{\mathbf{p}}}$ . For which values of n, m, r ,s, and p is the product${\mathbf{A}}\left(B\stackrel{\to }{x}\right)$defined?

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

See the step by step solution

## Step 1: Find the solutions of the systems

For m=r to be defined the number of columns of B must be equal the number of components of$\stackrel{\to }{x}$ .

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

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

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