PROBLEM 3: Consider the set s={A€M₂x3 (P (R): A = 0 с ab 0 , where a > 0, b>0, >>o, c>0}. with the usual matrix addition and matrix scalar multiplication. a) Give an example of an element in S. b) Show that S is closed under addition or give an example to show that it's not. c) Show that S is closed under scalar multiplication or give an example to show that it's not. d) Find a basis for S. Make sure to verify the requirements for a basis. e) Find dim[S].
PROBLEM 3: Consider the set s={A€M₂x3 (P (R): A = 0 с ab 0 , where a > 0, b>0, >>o, c>0}. with the usual matrix addition and matrix scalar multiplication. a) Give an example of an element in S. b) Show that S is closed under addition or give an example to show that it's not. c) Show that S is closed under scalar multiplication or give an example to show that it's not. d) Find a basis for S. Make sure to verify the requirements for a basis. e) Find dim[S].
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 26E
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Problem 3, please look at the attached image
![PROBLEM 3:
0 0 c
Consider the set S=
{A€M₂ x 3 (R): A =
-[88]
where a > 0, b>0,
+0,c>0} w
with the usual
a b 0
matrix addition and matrix scalar multiplication.
a) Give an example of an element in S.
b) Show that S is closed under addition or give an example to show that it's not.
c) Show that S is closed under scalar multiplication or give an example to show that it's not.
d) Find a basis for S. Make sure to verify the requirements for a basis.
e) Find dim[S].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdda4c31c-eb33-4b34-a3d5-bc34c938fa3d%2F79ad6caa-e08c-4e2d-9249-3316ad45711a%2F1z7oen7h_processed.png&w=3840&q=75)
Transcribed Image Text:PROBLEM 3:
0 0 c
Consider the set S=
{A€M₂ x 3 (R): A =
-[88]
where a > 0, b>0,
+0,c>0} w
with the usual
a b 0
matrix addition and matrix scalar multiplication.
a) Give an example of an element in S.
b) Show that S is closed under addition or give an example to show that it's not.
c) Show that S is closed under scalar multiplication or give an example to show that it's not.
d) Find a basis for S. Make sure to verify the requirements for a basis.
e) Find dim[S].
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