1 1 3 ; = [ 1;2]

Soustavy lineárních rovnic - Příklady k procvičení ) + y= y= [ ; ] ) + y= = ) y= y 0 y ; + = [ ;] ) y= + y= [ ;] ) + y= = ; ) y= = y ) y = y= 8) y= + y= 9) = 8 y 0) y=, y= ) a+ = a b ) = y 9 ) u ( ) v = v v u 9 0 ) y ) r s + = + = ) m n 8 + = ) a b= 9 0 8) u v 8 = 0 9) p = q p+ q= 0) + y= y ) = + y ) r s = r s 8 ) y = 0 ) a= b 8b+ a= ) t+ z= t z ) m n + = m n ) y 0 + = y 0 + = [ ; ] ; + = [ ; ] + = [ ; ] + = [ ; ] y= [ ; ] r s= [ ; ] m n= [ 8;0 ] b = [ ;9 ] u+ v= [ ;] ; = [ ;9 ] + y= [ ; ] + = [ ; ] + y= [ ;0] ; = [, ] = [ ; ] + = [ 0; ] Soustavy lineárních rovnic / 0

8) u= v v u = [ 0; ] 9) + y= ( y ) = y [ ; ] 0) ( p ) = q+ ( q ) = p+ [ ; ] + = ( ) ) y = 8 s 9r ) ( r s) + y= 0 + = [ 8;0] ) z= ( ) + 9 ( ) = + z [ ; ] ) 0, + 0,y=,, 0,y= [ 0; ] ) + y= ( y ) = y [ t, ),r 0,8s= r 0,s= 0,r [ ; ] ) + y= + y= [ 0; ] 8) a+ b= 8 a+ b= [ ; ] 9) p q= p q= [ ; ] 0) + y= + y= ; ) m+ 9n= 8 9m 8n= 9 [ ; ] ) r s= 0 s r= 8 [ 9, ] ) ( + ) = y ( ) = [ ;] ),+ 0,y= 9,, 0,9y= [ ; ] ) ( a+ b) ( a b) = ( a+ b) ( a b) = [ 9; ] ) ( + ) = ( ) ( ) = ( y ) [ 8; ] y ) + y= 8 u y 8) + y= 0 + 9) y= h 0) + = k k 8 h y y ) + = m n m n ) + = y y ) + = a b a b ) + = + = [ ; ] + = [ 0;8 ] = [ ; ] + = [ ; ] + = [ ; ] = [ 0, ] + = [ ;] = [ ;8 ] Soustavy lineárních rovnic / 0

) y + = = [ 8; ] u v u v ) = + = 8 [ 8;9 ] y y ) + = + = [ ;] p q p q 8) + = + = 9 9 [ ; ] + y 9) + y = = [ ; ] 0) + = y [ ;0 ] + y y ) = + y= 0 [ ; ] y y ) = + =, ; a b a+ b ) + = = 0 [ ; ] + y + ) = + y = [ ; ] y t+ ) = + y = t, 8 + y y ) + = y [ ; ] + t ) y =,= t, y + y 8) + = 0 = [ 0;8 ] t z+ 0 z 0 t 0 9) + = = 0 [ 0;0 ] + y 0) = + = [ ;8 ] + y y + ) = = [ ; ] a b+ a a+ b+ a+ b+ ) + = = [ ; ] y 9 ) = + = [ ; ] ) + y= y= y z ) + y= 8 y ) + y= y + = y y + = y z + = [ ;; ] = [ 0;8; ] + + = [ ;; ] Soustavy lineárních rovnic / 0

) + y= y= y z 8) a+ b+ c= a b 0 = a b 9) + y= y= 8 z= 0 80) + y= + z= y z 9 8) r+ s= 9 r t 0 8) a+ b= a c 8) u+ v= u z 8) + y= z = 0 + = s t + = b c = z v + + = [ 0;; ] + = [ ;8; ] 0 + = [ ;; ] + = [ ;; ] = [ ;; ] = [ 0;; ] y= 8) a= b a+ 0c= a b 0 8) + z= z 9 8) a+ b c= a b c = y z + = b c a 88) + y z= z= + z= + = [ ;;0, ] + = [ ;; ] + = [ ;8; ] 89) + y= + z z= z 0 90) r+ s t = r s t + + = r s t 0 9) a+ b+ c= a+ b+ c= a+ c= = [ 0;; ] + + = [ ;; ] 9) + z= 00 + 0y z= 0 y 0 ;; = [ ;;0 ] + z= [ 0;0;0 ] = [ ;; ] 9) 0, + 0,y 0, z= 0, 0, 0,z= 0, 0, 0, 9) y z= y z = z y y z z y 9) + = 8 + = 8 y z y z 9) + = + = 9 a b c a b c a b c 9) + + = + + = 8, y z z 98) = = y z z p q+ p q r 99) = = p r 00) y= y z= z = 0) u+ v= z+ v= u u+ v= 9z 0) + y= + z= y z 0 0) z= y = y z 0 + = [ ;;8 ] + = [ ;9; 0] + + = [ 0;;0 ] = [ ;; ] = [ ;; ] + = [ ;; ] + = [ t+ ; t; Soustavy lineárních rovnic / 0

0) + y= z= y z 0) y = [ 8;; ] z= [ ;; ] y z= [ ; ;] + = [ ; ] = [ ; ] + = + z= 0 0) y z + + = y z= 0) y 0 + = y 0 08) y 0 + = y 0 09) y= y= + 8 0) y= y 8 ) y + = y ) y = y 0 ) y 0 + = y 0 ) y + = = [ t+ ; + = [ 8; ] + = [ t;t+ ] + = [ ; ] + = 0 + y y y y ) + = = [ ; ] 8 0 ; ) + y= y= ) = y y= [ t; 8) + y= 0,y, 9) + y= 8 + = [ t, = y 0) + y= y ) y + = y 8 8 t t, = [ ; ] + = [ t; ) + y= + y= ) + y= + y= [ ;] ) ( + )( y ) = ( )( ) ( )( ) = ( + )( y ) [ ; ] ) = y + 0, = 0,+ 0,y ) y z= 0 y z ) + y z= 0 y z 0 8) y z t t,, t, t + + = ( + t) ( ) + + = [ 8 t, t; y z y z + = ( + ) = = ( ) [ ;; ] + = ( + ) = ( ) = ( + ) [ ;;88 ] 9) y z 8 0) + y= y = [ ;0 ] Soustavy lineárních rovnic / 0

) + y= 0 y ) y + = ) y + = ) y = ) y + = ) 9y = y= ) = y y= + = [ ; ] y= [ ; ] y= [ 0; ] + y= [ ; ] + y= [ 8; ] ; 8 ; 8) + y=, 8 y= 0, [ 0, ;0, ] 9) 0, + 0, y= 0, y= 0 [ 00;0 ] 0), 0,y=, 0, +, y= 9, [ ; ] ) + y 8= ( + y) y = ( y) [ ; ] ) ( + y) = ( + ) ( ) y = ; ) ( + y) + ( + y) = ( + y) ( y ) = [ ; ] ) 9( 0y) ( y ) = ( y) + 9 y= ( y) ( + y ) [ ; ] ) y= y= + ) y= y 9 ; = [ ; ] ) y= + y ( ) y y 8) + = 9) y y + = 0 8 0) y y + = 9 9 y y y y ) + + 0= + 0 + ) = y y ) + y= 8 8 ) y= ( y) y ( y) 8 = [ ;] + = [ ;] = [ 8; ] + = [ ; ] = [ 0;0 ] = [ ; ] + = [ ; ] = [ ; ] Soustavy lineárních rovnic / 0

) + = y y ) + = y ) ( y) y 8) 9 + + y y y = + y y y + 0 y 8 [ ; ] = [ ; ] + = ( ) = [ ; ] = ( + ) = [ ; ] 9) = ( ) = ( ) [ ; ] + = +z=0 z= [ ;; ] 0) y 9 ) y= y= ) = + y = ( y 0) ) -y= =9 +z=0 [ ;; ] ) y= z= z = ) + y= y= = 0 ) +z= -z= +y-z=8 [ ;; ] ) +z= +z=0 +z= [ ;; ] 8) +y-z=0 -y-8z=0 +z= [ ; ;] 9) +z= -z= +y-z= [ ;0;0 ] 0) 0,+0,80,z= 0,9-,0,z= 0,-y-0,z=-, [ ;; ] ) 0,-,0,z=0,8+0,y-0,z=,+,,= [ 0;0;0 ] ) ) y z + = 9 z = y z= 8 z+ y = 9 y z 9 + y z = + = [ ;; ] ) + y= z=9 +z=8 [ ;; ] ) +y=0 +z=9 y-z= [ ;; ] ) +z= +z=9 -z= [ ;0; ] ) + z= + z= +z= [ ; ;] 8) +z= +z= +z=- [ ;; ] 9) +z= +z= +89z= 00 Soustavy lineárních rovnic / 0

80) +y-z=- -z=0 +y-z=-9 8) +y-z= -+z= -+z= 8) +y-z= +z=0 +y-z= 8) +z= +y-z= +z= 8) +y=0 -y=0 [ 0,0 ] ;9 ;8 8) +y=-8 -y= [, ] 8) u-v= u-v=- [ ; ] 8) -8a+b= a-b=-9 [ t;t+ ] 88) c-d=9 -c+8d= 89) -y= -y= [ ; ] 90) +y= -y= [ ; ] 9) u-v=- u+v= [ ; ] 9) u+v= -u+v= 9) 0,+0,y=, 0,-0,y=0,9 [ ; ] ; 9 9 9) 0,y-0,z=0, 0,0,z=, [ ; ] 9) 0,m+0,n=0, 0,m-0,n=-0,8 [ ;] 9),r-0,8s=, 0,9r-0,s=,8 [ t;,t ] y y 9) + = + = [ ; ] y z y z 98) + = = 8 [ ; ] 99) u-v=0 u v + = ; 00) r+s= r s + = [ ;] 0) -y=0 + y = [ ; ] 0) 8-y= = ( ) u 0) v u v 8t u+ v = v t; 9 u v 0) + = 0 ( u+ v) = ( v+ ) [ ; ] 0) y 8 = = [ ;0 ] 0) u v= v u 0,; + = [ ] Soustavy lineárních rovnic 8 / 0

0) r+s= 08) 09) 0) p+ q = + = y = r s p = q = [ ; ] ( y) ( y ) = + ( y ) = u+ u ) = v v ) u+ v = = v u ) ) = + = + y ; = [ ; ] = y = ; [ ;] ; ) +y= +y= [ ; ] ) +y=- +y=- ; ) +y= +y= [ 8; ] 8) -y= -0y= 9) +y= +y= [ 9; ] 0) y=-+ y=-- ) =-0 = [ ; ] ) +y= -y= 8 ; ) +y= +y=9 [ ; ] ) -y=8 -y= [ ; ] ) y=-9 = [ 8; 9] ) -y-=0 -y-=0 ; ) +y=, +8y= [ ;;; ] 8) ( + y) ( y ) = ( + y) + ( + y) = [ ; ] 9) +y-8=(+y) -y-=(-y) [ ; ] 0) (+)(y-)=(-)() (+)(y-)=(-)() [ 8; ] ) (+)()=(+)(8) (-)()=(-)() [;] ) (+)(y-)=(+)(y-) (-)()=(-)() [;] ) (+y)-8(-y)=00 0(-y)-(-y)=0 [;] Soustavy lineárních rovnic 9 / 0

+ y y y ) + = ) + = y + = y [ ; ] + ( y) y ) = y ) y y y y + + + = y [ ; ] 8) y 9 = + = [ ; ] = [ ; ] = [ ; ] 9) ( ) ( ) = ( ) + ( ) = [ ; ] 0) ( + y) + ( y) = 8( + y) ( y) = [ ; ] ) +y=8 z+=0 z= [ ;; ] ) ) y= + y= y z= z= + z= z+ = ) +y=9 y-z=- z-= [ ;; ] ) +y= -z= y-z= [ 8;; ] ) +y= y-z=-9 z-=8 [;;] ) +y= +z= z=9 [;;] 8) + y z= -z= z-= [;8;] 9) -y-z= y--z= z--y=- [;;-] 0) +z=00 -z=0 +y-z=0 [;;] ) +z=0 +y-z=0 -z=0 [;;] ) +y-z=-8 -+z=0 -z= [;;] ) -z= +y-z=0 -+z=8 [0;;] ) +y-z=0 -y-8z=0 +z= [;-;] ) +z=0 -z=0 +y-z=0 [0;0;0] ) +y-z=0 +y-z= +y-z=0 [;;] y z ) 0 0 y z y z y z 8) + + = + + = + + = [;-0;0] z + z + y 9) = y = z = 9 = -0,+0,z= -y-z=- t; ( t ); ( t+ ) Soustavy lineárních rovnic 0 / 0