Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

True or false: (a) If A2 is defined then A is necessarily square. (b) If AB and BA are defined then A and Bare square. (c) If AB and BA are defined then AB and BA are square. (d) If AB

Sagot :

LammettHash

(a) True. Suppose A is a not a square matrix, with m rows and n columns. Then A² is not defined, because you can't multiply an m×n matrix by another m×n matrix.

(b) False. As an example, consider the matrices

[tex]A_{3\times2} = \begin{bmatrix}1&0\\0&1\\0&0\end{bmatrix}[/tex]

[tex]B_{2\times3} = \begin{bmatrix}-1&0&1\\0&0&1\end{bmatrix}[/tex]

Then both AB and BA are defined, with

[tex]AB_{3\times3} = \begin{bmatrix}-1&0&1\\0&0&1\\0&0&0\end{bmatrix}[/tex]

[tex]BA_{2\times2} = \begin{bmatrix}-1&0\\0&0\end{bmatrix}[/tex]

In general, you can multiply any m×n by any n×m matrix.

(c) True. Multiplying a m×n matrix by a n×m matrix always yields a m×m matrix, and multiplying a n×m matrix by a m×n matrix always yields a n×n matrix.

Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.