Prove property 6 is true by rearranging the flig 3X3 Property 6: for all mastuces A in U = M3x3 and for all real scalars C, C&A is in V=Mgx3 Suppose A is in V=M3x3 & c is a real # CA A must be in V =M3 x 3 By definition of C @ A, bij = c+aij C, aij are real #'s, bij is also a real # is a 3x3 matrix of real #'s COA Let al; and bij be the ijth entries of A and B = c A respectiv ans should be a string of letters ex FEDORA 20A)
Prove property 6 is true by rearranging the flig 3X3 Property 6: for all mastuces A in U = M3x3 and for all real scalars C, C&A is in V=Mgx3 Suppose A is in V=M3x3 & c is a real # CA A must be in V =M3 x 3 By definition of C @ A, bij = c+aij C, aij are real #'s, bij is also a real # is a 3x3 matrix of real #'s COA Let al; and bij be the ijth entries of A and B = c A respectiv ans should be a string of letters ex FEDORA 20A)
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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![## Vector Spaces
### Prove Property 6 is True by Rearranging the Following
**Property 6:** For all matrices \( A \) in \( V = M_{3 \times 3} \) and for all real scalars \( c \), \( c \otimes A \) is in \( V = M_{3 \times 3} \).
#### Steps:
A) Suppose \( A \) is in \( V = M_{3 \times 3} \) and \( c \) is a real number.
B) \( c \otimes A \) must be in \( V = M_{3 \times 3} \).
C) By definition of \( c \otimes A \), \( b_{ij} = c + a_{ij} \).
D) Since \( c, a_{ij} \) are real numbers, \( b_{ij} \) is also a real number.
E) \( c \otimes A \) is a \( 3 \times 3 \) matrix of real numbers.
F) Let \( a_{ij} \) and \( b_{ij} \) be the \( ij \)-th entries of \( A \) and \( B = c \otimes A \) respectively.
---
**Answer should be a string of letters, e.g., FEDCBA:**
\[ \_\_\_\_\_\_ \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe0243d8a-eca1-425a-958c-12b2dd6f68ba%2F76ce8b1d-3ded-4f82-be2c-c37d51dd3a2f%2Fac33q7o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Vector Spaces
### Prove Property 6 is True by Rearranging the Following
**Property 6:** For all matrices \( A \) in \( V = M_{3 \times 3} \) and for all real scalars \( c \), \( c \otimes A \) is in \( V = M_{3 \times 3} \).
#### Steps:
A) Suppose \( A \) is in \( V = M_{3 \times 3} \) and \( c \) is a real number.
B) \( c \otimes A \) must be in \( V = M_{3 \times 3} \).
C) By definition of \( c \otimes A \), \( b_{ij} = c + a_{ij} \).
D) Since \( c, a_{ij} \) are real numbers, \( b_{ij} \) is also a real number.
E) \( c \otimes A \) is a \( 3 \times 3 \) matrix of real numbers.
F) Let \( a_{ij} \) and \( b_{ij} \) be the \( ij \)-th entries of \( A \) and \( B = c \otimes A \) respectively.
---
**Answer should be a string of letters, e.g., FEDCBA:**
\[ \_\_\_\_\_\_ \]
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