Let A E Rx and B E Rmxm and assume that dim N(A) = k and dim N(B) = l. Let C be an 2 x 2 block diagonal matrix defined as Find dim N(C) C = | A Onxm B Omxn (n+m) x(n+m)
Let A E Rx and B E Rmxm and assume that dim N(A) = k and dim N(B) = l. Let C be an 2 x 2 block diagonal matrix defined as Find dim N(C) C = | A Onxm B Omxn (n+m) x(n+m)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let \( A \in \mathbb{R}^{n \times n} \) and \( B \in \mathbb{R}^{m \times m} \) and assume that \( \dim N(A) = k \) and \( \dim N(B) = \ell \). Let \( C \) be a \( 2 \times 2 \) block diagonal matrix defined as
\[
C = \begin{bmatrix} A & 0_{n \times m} \\ 0_{m \times n} & B \end{bmatrix}_{(n+m) \times (n+m)}.
\]
Find \( \dim N(C) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98b6e310-08ba-4e1d-a9bc-704b45d2ce6c%2Fa207530c-37aa-4461-bee5-2d367d379559%2Fvekpky4_processed.png&w=3840&q=75)
Transcribed Image Text:Let \( A \in \mathbb{R}^{n \times n} \) and \( B \in \mathbb{R}^{m \times m} \) and assume that \( \dim N(A) = k \) and \( \dim N(B) = \ell \). Let \( C \) be a \( 2 \times 2 \) block diagonal matrix defined as
\[
C = \begin{bmatrix} A & 0_{n \times m} \\ 0_{m \times n} & B \end{bmatrix}_{(n+m) \times (n+m)}.
\]
Find \( \dim N(C) \).
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