- #91
says
- 585
- 12
(0,1,-1,1) and (0,1,-1,-1)
Is There a Quicker Way to Find All Possible Values of h for fh(a+bx+cx2+dx3)?
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Homework Help Overview
The discussion revolves around finding all possible values of h in the context of a linear transformation represented by a 2x2 matrix derived from a polynomial of degree 3. The matrix is given as fh(a+bx+cx2+dx3) = [ a+b+c+hd b+c ] [ -b-c-hd hb ]. Participants are exploring the implications of h on the transformation and the relationships between the coefficients a, b, c, and d.
Discussion Character
- Exploratory, Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants discuss row reducing the matrix to derive equations involving h and question the assumptions made about the coefficients a, b, c, and d. There is uncertainty about the notation and the nature of the transformation, with some participants suggesting that h could take on multiple values depending on the context.
Discussion Status
The discussion is ongoing, with various interpretations of the problem being explored. Some participants have provided insights into the nature of linear transformations and the implications of h, while others express confusion about how to determine the values of h and the relationship to the kernel and image of the transformation.
Contextual Notes
There are indications of confusion regarding the notation and the setup of the problem, particularly concerning the nature of fh and the dimensionality of the transformation. Participants are also grappling with the implications of h on the linear transformation and how it relates to the kernel and image.