Reserved powers mainly involve rights stated in the Bill of Rights things that are referred to in the Supremacy Clause diplomatic powers to make treaties with other nations things that affect the quality of people's lives

It can be shown that the algebraic multiplicity of an eigenvalue \( \lambda \) is always greater than or equal to the dimension of the eigenspace corresponding to \( \lambda \). Find \( h \) in the matrix A below such that the eigenspace for \( \lambda=6 \) is two-dimensional. \[ \left[\begin{array}{rrrr}6 & -3 & 9 & 6 \\ 0 & 3 & h & 0 \\ 0 & 0 & 6 & 5 \\ 0 & 0 & 0 & 1\end{array}\right] \] The value of \( h \) for which the eigenspace for \( \lambda=6 \) is two-dimensional is \( h=\square \).

Find the derivitative \( y=\sqrt{x} \operatorname{cosec} \sqrt{x} \)

4. Which of the following ordered triples is the solution to the system of equations? Desmos Matrix Calcualator \[ \begin{array}{c}2 x+2 y-z=8 \\ 3 x-2 y+3 z=2 \\ 2 x+4 y-z=12\end{array} \]

Solve the system of equations. If the system has no solution, say that it is inconsistent. Graph the lines of the system. \( \begin{array}{l}3 x+y=3 \\ 6 x+2 y=-3\end{array} \) Select the correct choice below and, if necessary, fill in any answer boxes within your choice. A. The solution is \( x=\square \) and \( y=\square \). (Type integers or simplified fractions.) B. There are infinitely many solutions. Using ordered pairs, they can be expressed as \{( \( x, y \) ) \( \mid x=\square \), \( y \) is any real number \( \}. \) (Simplify your answer. Type an expression using y as the variable as needed.) C. The system is inconsistent.

8. Kelly and Katie are each solving the system of equations shown below on their own and are planning on comparing their answers afterward. \( y=-x+17 \) \( y=-2 x^{2}+7 x+81 \) Kelly thinks there is only one solution to the system of equations, and Katie thinks there are two solutions to the system of equations. Who is correct?