Cvičenia

13. Gaussovou eliminačnou metódou určte riešenia nasledovných sústav lineárnych rovníc.
a)

$$\begin{array}{rrrrrrr} & & x_2 & + & x_3 & = & 2 \\ -x_1 ... ...3 & = & 1 \\ x_1 & + & 2x_2 & + & x_3 & = & 1 \\ \end{array}$$

b)

$$\begin{array}{rrrrrrr} 6x_1 & - & x_2 & - & x_3 & = & 11 \\... ...= & 32 \\ -x_1 & - & 2x_2 & + & 6x_3 & = & 42 \\ \end{array}$$

c)

$$\begin{array}{rrrrrrr} 2x_1 & + & 3x_2 & + & 5x_3 & = & 10 ... ... & = & 3 \\ x_1 & + & 2x_2 & + & 2x_3 & = & 3 \\ \end{array}$$

d)

$$\begin{array}{rrrrrrr} 4x_1 & - & 3x_2 & + & 2x_3 & = & -4 ... ...= & -1 \\ 5x_1 & - & 3x_2 & + & 2x_3 & = & -3 \\ \end{array}$$

e)

$$\begin{array}{rrrrrrr} 5x_1 & - & 6x_2 & + & 4x_3 & = & 3 \... ...& = & 2 \\ 4x_1 & - & 5x_2 & + & 2x_3 & = & 1 \\ \end{array}$$

f)

$$\begin{array}{rrrrrrr} 5x_1 & + & 2x_2 & + & 3x_3 & = & -2 ... ...= & 0 \\ 3x_1 & + & 4x_2 & + & 2x_3 & = & -10 \\ \end{array}$$

g)

$$\begin{array}{rrrrrrrrr} 2x_1 & + & 2x_2 & - & x_3 & + & x_... ... 3x_1 & + & 3x_2 & - & 2x_3 & + & 2x_4 & = & 6 \\ \end{array}$$

h)

$$\begin{array}{rrrrrrrrr} 2x_1 & + & 3x_2 & + & 11x_3 & + & ... ... x_1 & + & x_2 & - & 3x_3 & + & 4x_4 & = & -3 \\ \end{array}$$

i)

$$\begin{array}{rrrrrrrrr} 2x_1 & + & 5x_2 & + & 4x_3 & + & x... ... 3x_1 & + & 8x_2 & + & 9x_3 & + & 2x_4 & = & 37 \\ \end{array}$$