Let W be the set of all 2 x 2 matrices of the form 0 [22] Z 1 Select one: where z > 0. Then: None of them O W is closed under addition, and W is not closed under scalar multiplication, and Wis a subspace of M2x2. W is closed under addition, and W is not closed under scalar multiplication, and Wis not a subspace of M₂x2. OW is closed under addition, and W is closed under scalar multiplication, and W is a subspace of M2x2. W is not closed under addition, and Wis closed under scalar multiplication, and Wis not a subspace of M2x2.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 4AEXP
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Let W be the set of all 2 x 2 matrices of the form
0
[22]
Z
1
Select one:
where z > 0. Then:
None of them
OW is closed under addition, and W is not
closed under scalar multiplication, and Wis
a subspace of M2x2.
W is closed under addition, and W is not
closed under scalar multiplication, and Wis
not a subspace of M₂x2.
OW is closed under addition, and W is closed
under scalar multiplication, and W is a
subspace of M2x2.
W is not closed under addition, and Wis
closed under scalar multiplication, and Wis
not a subspace of M2x2.
Transcribed Image Text:Let W be the set of all 2 x 2 matrices of the form 0 [22] Z 1 Select one: where z > 0. Then: None of them OW is closed under addition, and W is not closed under scalar multiplication, and Wis a subspace of M2x2. W is closed under addition, and W is not closed under scalar multiplication, and Wis not a subspace of M₂x2. OW is closed under addition, and W is closed under scalar multiplication, and W is a subspace of M2x2. W is not closed under addition, and Wis closed under scalar multiplication, and Wis not a subspace of M2x2.
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