Use the formula derived in Exercise to find the inverse of the rotation matrix
Interpret the linear transformation defined by geometrically. Explain.
The inverse of the matrix is, , the geometrical interpretation is,
Consider the matrix.
The inverse of the matrix is,
The matrix represents the rotation by an angle and scaling by a factor .
The inverse matrix represents the rotation by an angle and scaling by a factor .The geometrical representation is,
The inverse matrix is, with geometrical interpretation of linear
Let in all parts of this problem.
(a) Find the scalar such that the matrix fails to be invertible. There are two solutions; choose one and use it in parts (b) and (c).
(b) For the you choose in part (a), find a non-zero vector such that
(c) Note that the equation can be written as.
Check that the equation holds for your from part (a) and your from part (b).
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