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Shay10825
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Hello. I'm having some trouble with this problem. Any help would be greatly appreciated.
Consider B= (2x+3, 3x^2 +1, -5x^2 + x-1}
a) Prove that B is a basis for P_2
b) Express -x^2 - 2 as a linear combination of the elements of B
c) If t: P_2 -> P_2 is a linear transformation, and T(2x+3) = x^2 -1, T(3x^2 +1) = x^2 -2x, T(-5x^2 +x-1)= -x^2 +3x, compute T(-x^2 -2) 2. The attempt at a solution
a)
Since:
B spans P2 and B is linearly independent, B is a basis for P2
b)
B = {2x+3, 3x2+1, 5x2+x-1}
2x t 3 = a
3x2 +1 = b
-5x2 + x -1 = c
By inspection:
-x2 - 2 = 2c + 3b –a
-x2 - 2 = 2(-5x2 + x -1) + 3(3x2 +1) – (2x t 3)
c) I typed it in Microsoft Word and uploaded it here:
http://img340.imageshack.us/img340/6180/matrixtheorydj6.png
Thanks
Homework Statement
Consider B= (2x+3, 3x^2 +1, -5x^2 + x-1}
a) Prove that B is a basis for P_2
b) Express -x^2 - 2 as a linear combination of the elements of B
c) If t: P_2 -> P_2 is a linear transformation, and T(2x+3) = x^2 -1, T(3x^2 +1) = x^2 -2x, T(-5x^2 +x-1)= -x^2 +3x, compute T(-x^2 -2) 2. The attempt at a solution
a)
Since:
B spans P2 and B is linearly independent, B is a basis for P2
b)
B = {2x+3, 3x2+1, 5x2+x-1}
2x t 3 = a
3x2 +1 = b
-5x2 + x -1 = c
By inspection:
-x2 - 2 = 2c + 3b –a
-x2 - 2 = 2(-5x2 + x -1) + 3(3x2 +1) – (2x t 3)
c) I typed it in Microsoft Word and uploaded it here:
http://img340.imageshack.us/img340/6180/matrixtheorydj6.png
Thanks
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