Question: Let R[z], be a linear space with all polynomials p(x) = ax + bx+c(a,b,c e R) whose degree is no more than 2. Let
![Let R[z], be a linear space with all polynomialsp(x) = ax + bx+c(a,b,c R) whose degree is no more than 2. Let](https://dsd5zvtm8ll6.cloudfront.net/questions/2023/12/659007dfc4e46_1704027976321.jpg)
Let R[z], be a linear space with all polynomials p(x) = ax + bx+c(a,b,c e R) whose degree is no more than 2. Let L be the operator on R[z], defined by L(ar+bx+c) = (a +3b +6c) + (a-3b-4c)x+ (a+b+c) 3 (1) Find the matrix A representing L with respect to basis [1, 2r, 3x]; (2) Find the matrix B representing with respect to basis [1-2r+3r,-1+2r, - 1+3z); (3) Is the matrix A diagonalizable? Why?
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