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Let T: R³ R4 be the linear map given by T(x, y, z) = (x + 3y – 2z, x + 4y, x − 8z, 2x + 7y – 2z) Write down the matrix of T (with respect to the standard bases of R³ and R4). Reduce the matrix to echelon form and use this to find a basis for Ker(T). What is the dimension of Ker(T)?

Let T: R³ R4 be the linear map given by T(x, y, z) = (x + 3y – 2z, x + 4y, x − 8z, 2x + 7y – 2z) Write down the matrix of T (with respect to the standard bases of R³ and R4). Reduce the matrix to echelon form and use this to find a basis for Ker(T). What is the dimension of Ker(T)?

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.2: The Kernewl And Range Of A Linear Transformation
Problem 59E: Let T:R3R3 be the linear transformation that projects u onto v=(2,1,1). (a) Find the rank and...
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Let T : R³ → R4 be the linear map given by T(x, y, z) = (x + 3y – 2z, x + 4y, x − 8z, 2x + 7y − 2z) Write down the matrix of T (with respect to the standard bases of R³ and R4). Reduce the matrix to echelon form and use this to find a basis for Ker(T). What is the dimension of Ker(T)?
Transcribed Image Text:Let T : R³ → R4 be the linear map given by T(x, y, z) = (x + 3y – 2z, x + 4y, x − 8z, 2x + 7y − 2z) Write down the matrix of T (with respect to the standard bases of R³ and R4). Reduce the matrix to echelon form and use this to find a basis for Ker(T). What is the dimension of Ker(T)?
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