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Unformatted text preview: 2. Consider the (ordered) bases = (1 ,x,x 2 ) and = ( x 2 + 1 ,x, 2 x 2 + x-1). (a) (5 pts) Compute [ L ] , the matrix representing L relative basis . (b) (10 pts) Compute [ L ] , the matrix representing L relative basis . (c) (8 pts) Compute P , the matrix changing -coordinates to -coordinates. (d) (2 pts) What are the kernel and image of L ? Clearly label which is which. (4) (10 pts) Let P k be real polynomials of degree k , and L : P 1 P 2 be integration (without arbitrary constant). For example, L (1) = x . Let = ( x + 1 ,x-1) and = ( x 2 + 1 ,x + 1 , 2 x 2-1) be (ordered) bases for P 1 ,P 2 respectively. Find [ L ] . 1...
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- Spring '07