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Let P, be set of all polynomials of degree atmost n. Let T: P2 defined by T(p(t)) = p(t) + 2t²p(t). P, be a transfomatien (a). Show that T is linear transformation. (b). Determine T is invertible or not. (c). Find the matrix for T relatíve to the bases {t,1+ t,t + e} and {1,t,r.7.)

Let P, be set of all polynomials of degree atmost n. Let T: P2 defined by T(p(t)) = p(t) + 2t²p(t). P, be a transfomatien (a). Show that T is linear transformation. (b). Determine T is invertible or not. (c). Find the matrix for T relatíve to the bases {t,1+ t,t + e} and {1,t,r.7.)

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 16CM
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Let P, be set of all polynomials of degree atmost n. Let T: P P, be a transformatiun defined by T(p(t)) = p(t) + 2t?p(t). II (a). Show that T is linear transformation. (b). Determine T is invertible or not. (c). Find the matrix for T relative to the bases {t, 1 + t,t + B} and {1,t,r,r,t}
Transcribed Image Text:Let P, be set of all polynomials of degree atmost n. Let T: P P, be a transformatiun defined by T(p(t)) = p(t) + 2t?p(t). II (a). Show that T is linear transformation. (b). Determine T is invertible or not. (c). Find the matrix for T relative to the bases {t, 1 + t,t + B} and {1,t,r,r,t}
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