Show solution on paper please! Let Mn.n(R) denote the vector space of n x n matrices with real entries. Let f : M2.2(R) → R be thefunction defined by f(A) = det (A) for any A E M2,2(R). Is f a linear transformation?[b11 b12][b21 b22.а11a12Let A =and B =be any two matrices in M2.2(R) and let c ER.a21а22.a. f(A+ B) = -(a12 a21 + b12 a21 + a12b21 + b12 b21)(Enter a11 as a11,etc.)f(A) + f(B) = (a11a22 - a12 a21)+ (b11b22 - b12b21)Does f(A+ B) = f(A)+ f(B) for all A, B E M2,2(R)? Yes, they are equalb. f(cA) =c(f(A) :Does f(cA) = c(f(A)) for all c E R and all A E M2,2(R)? Yes, they are equalc. Is f a linear transformation? f is a linear transformation

Answered: Image /qna-images/answer/c2b050e9-23b5-4a65-a54b-b1daf483a9bf.jpg

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 M2.2(R). Is f a linear transformation? [b11 b12 | b21 b22] a11 а12 Let A be any two matrices in M2.2(R) and let c E R. and B = a22 a21 a. f(A+ B) = -(a12 a21 + b12 a21 + a12b21 + b12 b21) · (Enter a11 as a11, etc.) f(A) + f(B) = (a11a22 - a12 a21) + (b11b22 - b12b21) Does f(A+ B) = f(A) + f(B) for all A, B E M2,2(R)? Yes, they are equal b. f(cA) = c(f(A)) =|| Does f(cA) = c(f(A)) for all c ER and all A E M2,2(R)? Yes, they are equal %3D c. Is f a linear transformation? f is a linear transformation

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 M2.2(R). Is f a linear transformation? [b11 b12 | b21 b22] a11 а12 Let A be any two matrices in M2.2(R) and let c E R. and B = a22 a21 a. f(A+ B) = -(a12 a21 + b12 a21 + a12b21 + b12 b21) · (Enter a11 as a11, etc.) f(A) + f(B) = (a11a22 - a12 a21) + (b11b22 - b12b21) Does f(A+ B) = f(A) + f(B) for all A, B E M2,2(R)? Yes, they are equal b. f(cA) = c(f(A)) =|| Does f(cA) = c(f(A)) for all c ER and all A E M2,2(R)? Yes, they are equal %3D c. Is f a linear transformation? f is a linear transformation

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter6: Vector Spaces

Section: Chapter Questions

Problem 16RQ

See similar textbooks