91Ó°ÊÓ

Evaluate, showing the details of your work. $$\left|\begin{array}{rrr} 70.4 & 0.3 & 0.8 \\ 0 & 0.5 & 2.6 \\ 0 & 0 & -1.9 \end{array}\right|$$

Solve the following systems or indicate the nonexistence of solutions. (Show the details of your work.) $$\begin{aligned} 4 y+4 z &=24 \\ 3 x-11 y-2 z &=-6 \\ 6 x-17 y+z &=18 \end{aligned}$$

Evaluate, showing the details of your work. $$\left|\begin{array}{rrr} 2 & 1 & 2 \\ -2 & 2 & 1 \\ 1 & 2 & -2 \end{array}\right|$$

Find the inverse by Gauss-Jordan [or by \(\left.\left(4^{\circ}\right) \text { if } n=2\right]\) or state that it does not exist. Check by using (1). $$\left[\begin{array}{ccc}0 & 8 & 0 \\\0 & 0 & 4 \\\2 & 0 & 0\end{array}\right]$$

Is the given set (taken with the usual addition and scalar multiplication) a vector space? (Give a reason.) If your answer is yes, find the dimension and a basis. All fanctions \(f(x)=a \cos x+b \sin x\) with any constants \(a\) and \(b\).

Evaluate, showing the details of your work. $$\left|\begin{array}{ccc} 0 & 3 & -1 \\ -3 & 0 & -4 \\ 1 & 4 & 0 \end{array}\right|$$

Find the inverse by Gauss-Jordan [or by \(\left.\left(4^{\circ}\right) \text { if } n=2\right]\) or state that it does not exist. Check by using (1). $$\left[\begin{array}{ccc}1 & 2 & 5 \\\0 & -1 & 2 \\\2 & 4 & 10\end{array}\right]$$

Find the inverse by Gauss-Jordan [or by \(\left.\left(4^{\circ}\right) \text { if } n=2\right]\) or state that it does not exist. Check by using (1). $$\left[\begin{array}{rrr}1 & 2 & -9 \\\\-2 & -4 & 19 \\\0 & -1 & 2\end{array}\right]$$

Is the given set (taken with the usual addition and scalar multiplication) a vector space? (Give a reason.) If your answer is yes, find the dimension and a basis. All \(2 \times 3\) matrices with the second row any multiple of \(\left[\begin{array}{lll}4 & 0 & -9\end{array}\right]\).

Evaluate, showing the details of your work. $$\left|\begin{array}{ccc} 0 & a & b \\ -a & 0 & c \\ -b & -c & 0 \end{array}\right|$$