Use the system of linear equation solving capabilities of Maple or another appropriate software package in Exercise.
a) Show that
x6 – x5 + 3x + 1, x5 + x4 + x2 + x + 1,
–x6 + x4 + x3 + 3x2 + x + 1,
2x6 – x4 – 2x3 – 5x2 – 1,
3x6 + x5 4–2x4 + x3 – x2 – x – 1,
x6 + 3x5 + 2x4 – 3x3 + 2x2 – 2x – 1,
2x6 – x5 + 2x3 + x2 – 3x + 1 form a basis for P6.
b) Find the coordinates of 7x6 + 6x5 – 5x4 – 4x3 3x2 + 2x – 1 relative to the basis in part (a).
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