Let P2 denote the vector space of all polynomials in the variable z of degree less than or equal to 2. Let C = {2, –2 + 3x, -3 – x – 3x²} be an ordered basis for P2. a. Write –1 – 10x – 3x? as a...

Please solve and answer in the same format as the question as it makes it easier to follow. Box answers and do not type it out and I will give you a thumbs up rating if answered correctly.

Chapter 4.1 Question 11

Extracted text: Let P2 denote the vector space of all polynomials in the variable z of degree less than or equal to 2. Let C = {2, –2 + 3x, -3 – x – 3x²} be an ordered basis for P2. a. Write –1 – 10x – 3x? as a linear combination of elements from the basis C. - - -1 – 10x – 3x² (2)+ 8, (-2+3x)+ , (-3 – x – 3x²). b. Let [g]c denote the coordinate representation of q relative to the basis C. Find the coordinate vector representation for –1 – 10x – 3x2 relative to the basis C. Your answer should be a vector of the general form <1,2,3>. [-1 – 10x – 3x²]c =