Q52E Consider a p 脳 n matrix A and a... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 3: Q52E (page 121)

Consider a p 脳 n matrix A and a q 脳 m matrix B, and form the block matrix $C = [\begin{matrix} A \\ B \end{matrix}]$ . What is the relationship between ker(A), ker(B), and ker(C)?

Short Answer

Expert verified

$\ker (C) 鈯� \ker (A) and \ker (C) 鈯� \ker (B)$

Step by step solution

Step 1: Objective

Consider a p 脳 n matrix A and a q 脳 m matrix B, and form the block matrix $C = [\begin{matrix} A \\ B \end{matrix}]$ . The objective is to find the relationship among ker(A), ker(B), and ker(C).

Step 2:The relationship among ker(A), ker(B), and ker(C).

$Let a vector \overset{鈫�}{w} be in the \ker (C) . C \overset{鈫�}{w} = \overset{鈫�}{0} [\begin{matrix} A \\ B \end{matrix}] \overset{鈫�}{w} = \overset{鈫�}{0} So, A \overset{鈫�}{w} = 0 and B \overset{鈫�}{w} = 0 . Hence, the vector \overset{鈫�}{w} is also in \ker (A) and \ker (B) . Thus, every vector in \ker (C) is also in \ker (A) and \ker (B) . Therefore, \ker (C) 鈯� \ker (A) and \ker (C) 鈯� \ker (B) .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Consider a p 脳 n matrix A and a q 脳 m matrix B, and form the block matrix $C = [\begin{matrix} A \\ B \end{matrix}]$ . What is the relationship between ker(A), ker(B), and ker(C)?

Short Answer

Step by step solution

Step 1: Objective

Step 2:The relationship among ker(A), ker(B), and ker(C).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

91影视

Consider a p 脳 n matrix A and a q 脳 m matrix B, and form the block matrix C=[AB]. What is the relationship between ker(A), ker(B), and ker(C)?

Short Answer

Step by step solution

Step 1: Objective

Step 2:The relationship among ker(A), ker(B), and ker(C).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Decision Maths

Study anywhere. Anytime. Across all devices.

Consider a p 脳 n matrix A and a q 脳 m matrix B, and form the block matrix $C = [\begin{matrix} A \\ B \end{matrix}]$ . What is the relationship between ker(A), ker(B), and ker(C)?