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Give an example of the described object or explain why such an example does not exist....

Give an example of the described object or explain why such an example does not exist.

•An orthogonal linear transformation T: R2→R2.

•An orthogonal linear transformation T: R3→R3.

•A basis B for R2 and an orthogonal linear transformation T: R2→R2 such that [T]B is an orthogonal matrix.

•A basis B for R2 and an orthogonal linear transformation T: R2→R2 such that [T]B is NOT an orthogonal matrix.

•A non-orthogonal linear transformation that takes an orthogonal basis to an orthogonal basis.

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