Let R[z], be a linear space with all polynomials p(x) = ax + bx+c(a,b,c e R)...

  

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Let R[z], be a linear space with all polynomials p(x) = ax² + 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(ar²+bx+c) = (a +3b +6c)² + (a-3b-4c)x+ (a+b+c) 3 (1) Find the matrix A representing L with respect to basis [1, 2r, 3x²]; (2) Find the matrix B representing with respect to basis [1-2r+3r²,-1+2r, - 1+3z²); (3) Is the matrix A diagonalizable? Why? Let R[z], be a linear space with all polynomials p(x) = ax² + 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(ar²+bx+c) = (a +3b +6c)² + (a-3b-4c)x+ (a+b+c) 3 (1) Find the matrix A representing L with respect to basis [1, 2r, 3x²]; (2) Find the matrix B representing with respect to basis [1-2r+3r²,-1+2r, - 1+3z²); (3) Is the matrix A diagonalizable? Why?

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Here are the answers to the given prompts 1 Matrix A representing L with respect to basis 1 2 3x2 Ap... View the full answer