Verify that the standard matrix of the projection onto W in Example 7.31 (as constructed by Theorem

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Verify that the standard matrix of the projection onto W in Example 7.31 (as constructed by Theorem 7.11) does not depend on the choice of basis. Take
Verify that the standard matrix of the projection onto W

as a basis for W and repeat the calculations to show that the resulting projection matrix is the same.

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