Let Mn.n(R) denote the vector space of n x n matrices with real entries. Let f : M2.2(R) → M2.2(R) be the function defined by f(A) = A" for anyA E M2,2(R). Is f a linear transformation?b12[b1[b21а11a12Let Aand B :be any two matrices in M2.2(R) and let c E R.а21а22b2.a. f(A+ B) =(Enter a11 as a11, etc.)f(A) + f(B)Does f(A+ B) = f(A) + f(B) for all A, B E M22(R)? chooseb. f(cA) =c(f(A)) =Does f(cA) = c(f(A)) for all c E R and all A E M2,2(R)? choosec. Is fa linear transformation? choose

Introduction: A linear transformation is a function from one vector space to another that preserves…

Let Mn.n(R) denote the vector space of n x n matrices with real entries. Let f : M22(R) → M22(R) be the function defined by f(A) = AT for any A E M22(R). Is fa linear transformation? [b11 b12] [b21 b2. [a11 a12] Let A = and B = a22 be any two matrices in M2.2(R) and let c E R. a21 a. f(A+ B) = - (Enter a11 as a11, etc.) f(A) + f(B) = Does f(A+ B) = f(A) + f(B) for all A, B E M2,2(R)? choose b. f(cA) =