about orthogonal matrix , orthogonal complement, and orthogonal projections, please with clear writing with steps

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1. In Chapter five, Locke presents an argument for man’s natural right to private property. What is that argument? What does he conclude that such a right consists in? What is the end, origin and extent of that right for man originally, and for man as he is presently situated? Is it natural to all men? Is it limited in scope? Has the right changed over time? What occasioned that change, if it did in fact alter? Does man have a right to unlimited acquisition of private property according to Locke?

2. For Locke, all power that one man has over another man is a limited power. Why is such power always limited? He further argues in the case of such particular modes of such a power that the limits, origin and ends of the power is different, why? In the case of parental power, spousal power, and political power, why is each of these powers limited in its own peculiar manner? Present how he argues that political power, his principal concern, is limited. Present how and why the other forms of power over an other is limited in their own manner.

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