(a) Suppose the coefficient matrix is \( A=\left[\begin{array}{cc}4 & 5 \\ -3 & -4\end{array}\right] \). Find \( A^{-1} \) and use it to write the solution matrix \( \left[\begin{array}{l}x \\ y\end{array}\right] \) as a product of two matrices. \[ \left[\begin{array}{c}x \\ y\end{array}\right]= \]

14. Uttrycken nedan har samma positiva värde på \( a \). Vilka tal ska stå i rutorna så att likheterna stämmer? \( a^{\frac{1}{3}}=\square \quad a^{\frac{2}{3}}=9 \)

5. Bestäm värdet på \( a \) så att olikheten \( 2 x-a<5 \) har lösningen \( x<7 \)

Find the nth term of the geometric sequence whose initial term is \( a_{1}=5 \) and common ratio is 10 . \( a_{n}=\square \) Next Question answer must be a function of \( n \).) .

Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another meth Write all numbers as integers or simplified fractions. \[ \begin{array}{l}7 x+7 y=-19 \\ \\ -9 x-5 y=4 \\ \text { Part: } 0 / 2 \\ \text { Part } 1 \text { of } 2 \\ \text { Evaluate the determinants } D_{1} D_{x} \text {, and } D_{y} \\ D=\square\end{array} \] \( \square \)

Use the elimination method to find all solutions of the system: \( \left\{\begin{array}{l}x^{2}-2 y=7 \\ x^{2}+5 y=14\end{array}\right. \) The two solutions of the system are: (the one with \( x<0 \) is) \( x=\square \) \( y=\square \) (the one with \( x>0 \) is) \( x=\square \) \( y=\square \)