Suppose f(en) = an for n = 1,2 and f is a linear transformation. y 3...

 

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Suppose f(en) = an for n = 1,2 and f is a linear transformation. y 3 3 2 2 e2 el -1 -1 a1 -2 -2 -3 -3 -2 -1 -3 -3 -2 -1 1 2 3 2 Domain Codomain a. Find a formula for f. Your answer should be a coordinate vector with the variables r and y in its components. f(x, y) = b. Find the matrix for the linear transformation f (relative to the standard basis in the domain and codomain). That is, find the matrix A such that f(x)= Ax. For instance, 1 2 3 4 enter [ [1,2], [3,4] ] for the matrix A = c. Find the kernel of f. Enter your answer as a vector with constant entries, a vector with the variables r or y (or both) in its components (using a minimum number of variables), or enter R^2 for R?. ker(f) = d. Find the image of f. Enter your answer as a vector with constant entries, a vector with the variables I or y (or both) in its components (using a minimum number of variables), or enter R^2 for R2 im (f) = e. The linear transformation f is (select all that apply): A. surjective (onto) O B. injective (one-to-one) O C. bijective (an isomorphism) O D. none of these Suppose f(en) = an for n = 1,2 and f is a linear transformation. y 3 3 2 2 e2 el -1 -1 a1 -2 -2 -3 -3 -2 -1 -3 -3 -2 -1 1 2 3 2 Domain Codomain a. Find a formula for f. Your answer should be a coordinate vector with the variables r and y in its components. f(x, y) = b. Find the matrix for the linear transformation f (relative to the standard basis in the domain and codomain). That is, find the matrix A such that f(x)= Ax. For instance, 1 2 3 4 enter [ [1,2], [3,4] ] for the matrix A = c. Find the kernel of f. Enter your answer as a vector with constant entries, a vector with the variables r or y (or both) in its components (using a minimum number of variables), or enter R^2 for R?. ker(f) = d. Find the image of f. Enter your answer as a vector with constant entries, a vector with the variables I or y (or both) in its components (using a minimum number of variables), or enter R^2 for R2 im (f) = e. The linear transformation f is (select all that apply): A. surjective (onto) O B. injective (one-to-one) O C. bijective (an isomorphism) O D. none of these

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Answer Anss a We have e 10 e2 0a1 and ... View the full answer