Let 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) = det (A) for anyA E M2,2(R). Is f a linear transformation?b12be any two matrices in M2.2(IR) and let c E R.b22a12[b1a11Let A =and Bа21а22.b21a. 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(IR)? 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

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Let 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) = det(A) for any A E M22(R). Is f a linear transformation? [a11 a12] Let A = a21 [b11 b12 [b21 b22 and B = a22 be any two matrices in M2.2(R) and let c E R. а. f(A + B) %3D (Enter a11 as a11, etc.) f(A) + f(B) + Does f(A+ B) = f(A) + f(B) for all A, B e M22(R)? choose b. f(cA) = c(f(A) : Does f(cA) = c(f(A)) for all c E R and all A E M22(R)? choose c. Is fa linear transformation? choose

Let 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) = det(A) for any A E M22(R). Is f a linear transformation? [a11 a12] Let A = a21 [b11 b12 [b21 b22 and B = a22 be any two matrices in M2.2(R) and let c E R. а. f(A + B) %3D (Enter a11 as a11, etc.) f(A) + f(B) + Does f(A+ B) = f(A) + f(B) for all A, B e M22(R)? choose b. f(cA) = c(f(A) : Does f(cA) = c(f(A)) for all c E R and all A E M22(R)? choose c. Is fa linear transformation? choose

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section6.4: Linear Transformations

Problem 34EQ

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