Cvičenia

15. Zistite, či nasledujúce sústavy sú riešiteľné a ak áno, nájdite ich riešenie.
a)

$$\begin{array}{rrrrrrr} x_1 & + & 2x_2 & - & 8x_3 & = & 1 \... ...= & 0 \\ 3x_1 & + & 2x_2 & - & 12x_3 & = & 0 \\ \end{array}$$

b)

$$\begin{array}{rrrrrrr} 3x_1 & - & x_2 & + & x_3 & = & -2 \... ...& = & 6 \\ 2x_1 & + & 3x_2 & + & x_3 & = & 0 \\ \end{array}$$

c)

$$\begin{array}{rrrrrrr} 7x_1 & - & 4x_2 & - & 2x_3 & = & -6 \\ 16x_1 & + & 2x_2 & + & x_3 & = & 3 \\ \end{array}$$

d)

$$\begin{array}{rrrrrrr} x_1 & - & 3x_2 & + & 2x_3 & = & 2 \\ 5x_1 & - & 15x_2 & + & 7x_3 & = & 10 \\ \end{array}$$

e)

$$\begin{array}{rrrrrrrrr} 3x_1 & - & 6x_2 & - & x_3 & - & x... ... 2x_1 & - & 4x_2 & + & 3x_3 & - & x_4 & = & 3 \\ \end{array}$$

f)

$$\begin{array}{rrrrrrrrr} 4x_1 & + & 3x_2 & - & 9x_3 & + & ... ... 3x_1 & - & x_2 & + & 8x_3 & - & 2x_4 & = & -7 \\ \end{array}$$

g)

$$\begin{array}{rrrrrrrrr} x_1 & + & 2x_2 & + & 3x_3 & + & 4... ...3x_1 & + & 5x_2 & + & 6x_3 & + & 13x_4 & = & 5 \\ \end{array}$$

h)

$$\begin{array}{rrrrrrrrrrr} x_1 & + & x_2 & - & x_3 &&&&& =... ... x_2 & - & 4x_3 & + & 5x_4 & - & 9x_5 & = & -5 \\ \end{array}$$