3 separate problems. The first two are missing one part. Thank you so much for your help and please show you work.

\fLet f : R2 -> R be defined by f((x, y) ) = -4x - 6y. Is f a linear transformation? a. f((x1, y1) + (x2, 92) ) = -4x1 - 6yl - 4x2 - 6v2 . (Enter x1 as x1, etc.) f ((x1, y1)) + f((x2, y2)) = -4x1 -6yl + -4x2 - 612 Does f( (x1, y1) + (x2, 92)) = f( (x1, y1)) + f((x2, 32)) for all (x1, y1), (x2, 92) E R2? Yes, they are equal v b. f(c(x, y) ) = c(-4x - 6y) c(f ((z, y)) ) = Does f(c(x, y)) = c(f((x, y) )) for all c E R and all (x, y) E R2? Yes, they are equal v c. Is f a linear transformation? fis a linear transformation v VLet Mn,n(R) denote the vector space of n x n matrices with real entries. Let f : M2,2(R) - R be the function defined by f(A) = trace(A) for any A E M2,2(R). Is f a linear transformation? Let A = all a12 and B = b11 612 be any two matrices in M2,2(R) and let c E R. a21 a22. b21 622. a. f( A + B) = [all + bll, a21 + 621, a12 + b12, a22 + 622] . (Enter an as all, etc.) f(A) + f(B) = + Does f(A + B) = f(A) + f(B) for all A, BE M2,2(R)? choose b. f(CA) = c(f( A)) = Does f(CA) = c(f(A)) for all c E R and all A E M2,2(R)? choose c. Is f a linear transformation? choose