1. Let T be a linear operator on P_3 defined as follows:
T(ax^3 + bx^2 + cx + d) = (a – b)x^2 + (c – d)x + (a +
b – c).
The matrix [T]_G which represents T with respect to the basis G which =
{1 + x, 1 – x, 1 – x^2, 1 – x^3}. Show that the standard matrix
representation and the preceding matrix representation are similar. Show
work.
Mathematics Homework Solutions
#12941
Matrix Representation : Linear Transformation
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Let T be a linear operator on P_3 defined as follows:
T(ax^3 + bx^2 + cx + d) = (a - b)x^2 + (c - d)x + (a + b - c).
The matrix [T]_G which represents T with respect to the basis G which = {1 + x, 1 - x, 1 - x^2, 1 - x^3}. Show that the standard matrix representation and the preceding matrix representation are similar. Show work.
Matrices are shown to be similar. The solution is detailed and well presented.
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