Cvičenia

14. Určte netriviálne riešenia nasledovných sústav homogénnych rovníc
a)

$$\begin{array}{rrrrrrrrr} 0x_1 & + &0x_2 & + & 0x_3 & + & 0x_4 & = & 0 \\ \end{array}$$

b)

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

c)

$$\begin{array}{rrrrrrrrr} 9x_1 & + &21x_2 & - & 15x_3 & + &... ...2x_1 & + &28x_2 & - & 20x_3 & + & 7x_4 & = & 0 \\ \end{array}$$

d)

$$\begin{array}{rrrrr} 2x_1 & + & 3x_2 & = & 0 \\ 3x_1 & - & x_2 & = & 0 \\ \end{array}$$

e)

$$\begin{array}{rrrrr} 2x_1 & + & 3x_2 & = & 0 \\ 4x_1 & + & 6x_2 & = & 0 \\ \end{array}$$

f)

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

g)

$$\begin{array}{rrrrrrr} 5x_1 & + & 2x_2 & - & 18x_3 & = & 0 \\ 2x_1 & + & x_2 & - & 8x_3 & = & 0 \\ \end{array}$$

h)

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

i)

$$\begin{array}{rrrrrrrrr} x_1 & - & 3x_2 & - & 26x_3 & + & ... ... 4x_1 & + & 5x_2 & - & 2x_3 & + & 3x_4 & = & 0 \\ \end{array}$$

j)

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