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Homework Statement
The set of all matrices A2x2 forms a vector space under the normal operations of matrix + and Scalar multiplication. Does the set B2x2 of all symmetric matrices form a subspace of M2x2? Explain.
Homework Equations
AT = A
Closure property of addition - If w and v are objects in A, then w+v are contained within A
Closure property of scalar multiplication - If K is any real number scalar and v is any object in A, then kv is also in A
The Attempt at a Solution
To be a subspace it must pass two axioms
1. B2x2 = [a,b;b,d] [a,b;b,d] + [e,f;g,h] = [a+e,b+f;b+g,d+h] I thought that this failed because it was not symmetric, but does it matter if the answer isn't symmetric only that its contained within A2x2
2. Scalar multiplication passes