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Linear Spaces, Mappings and Dimensional Spaces1) Show that if dim X = 1 and T belongs to L(X,X), there exists k in K st Tx=kx for all x in X.
2) Let U and V be finite dimensional linear spaces and S belong to L(V,W), T belong to L(U,V). Show that the dimension of the null space of ST is less than or equal to the sum of the dimensions of the null spaces of S and T.
3) Show that is X is a finite dimensional space then the space L(X,X) of all linear maps of X into X is finite dimensional. Find the dimension of L(X,X).
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The trigonometric function to find exact value.
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You have just graduated from college, and you have started your first big project at your new job. Your boss informs you that you are responsible for the Equations and Inequalities section of the project and for presenting your ideas to the team.
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Use the given information to draw the graph of f(x) on an interval near the indicated point (x=3). If there is not enough information given, then state this fact.
When graphing a linear inequality, how do you select the area (which side of the line) that is being represented (and has to be shaded) by the inequality?
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