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Homework Statement
Determine whether all 2x2 matrices with det(A) = 0 are a subspace of M2x2, the set of all 2x2 matrices with the standard operations of addition and scalar multiplication.
Homework Equations
Must pass in order to be a subspace
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
I wasn't sure where to really start with this one so I picked a matrix with a determinant of 0
B2x2 = [[w1,w2][w1,w2] and added it to another det=0 matrix C2x2 = [[v1,v1][v2,v2]]
Added together they make D2x2 = [[w1+v1,w2+v1][w1+v2,w2+v2]] which wouldn't have a det of 0 so this wouldn't be a subspace right?