Please solve it on paper 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 byf(A) = det(A) for any A E M2,2(IR). Is ƒ a linear transformation?[b11 b12]b21 b2.a11a12Let Aand Ba22.be any two matrices in M2.2(R) and let c E R.а21a. 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)) =%3DDoes f(cA) = c(f(A)) for all c E R and all A E M2,2(R)? Yes, they are equalc. Is fa linear transformation? f is a linear transformation

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1) = det(A) for any A E M2,2(R). Is ƒ a linear transformation? [b11 b12] [b21 b22 a12 A = a21 and B = а22 be any two matrices in M2.2(R) and let c E R. 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 c. Is f a linear transformation? f is a linear transformation

1) = det(A) for any A E M2,2(R). Is ƒ a linear transformation? [b11 b12] [b21 b22 a12 A = a21 and B = а22 be any two matrices in M2.2(R) and let c E R. 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 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

Section6.4: Linear Transformations

Problem 24EQ

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