Is the set of all 2x2 matrices of the form (see below) a vector space?

Question

[a 1]
[1 b]
Asume that a and b can be any number.
Verify your conclusion. Im having a bit of a hard time with this. The book doesn't show an example/definitions of what this is.

Answer 1

No it is not a vector space because it is not closed under addition or scalar multiplication.You actually need to show one only



Take

[a 1].................[c 1]

[1 b] and..........[1 d] in V





where a,b,c and d are any numbers

Their sum is



[a+c 2]

[2 b+d] does not belong to V.



Actually I think they mean to ask you to show that the set of the matrices of the given form is a not a vector subspace of M2x2

Answer 2

truly this set is a vector area: you may can upload 2x2 matrices to get different 2x2 matrices, there is an additive identity, and also you may multiply matrices by using scalars. to coach the area is finite dimensional you'll locate a foundation. the most obvious determination for a foundation is the 4 element set of matrices each and each and every having a million in a unmarried get entry to, and 0 in the different 3 entries. consequently the length is 4.

Answer 3

Consult Wikipedia for the definition of vector space. A VS requires 8 axioms

which are comparatively easy to verify in your example.