(Solution) - Consider the linear transformation of R3 represented with respect to -(2025 Original AI-Free Solution)

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Consider the linear transformation of R3 represented with respect to the standard bases by this matrix.

(a) Compute the determinant of the matrix. Does the transformation preserve orientation or reverse it?
(b) Find the size of the box defined by these vectors. What is its orientation?

(c) Find the images under t of the vectors in the prior item and find the size of the box that they define. What is the orientation?