pr 3
public text v1 · immutable> A3:=matrix(3,3,[1,0,0,0,1,0,0,0,0]);
[1 0 0]
[ ]
A3 := [0 1 0]
[ ]
[0 0 0]
> A4 := matrix(3, 3, [1, 0, 0, 0, 1, 0, 0, 0, 0])
[1 0 0]
[ ]
A4 := [0 1 0]
[ ]
[0 0 0]
Com t'expliques que tinguin la mateixa forma?
Tenen la mateixa forma perquè utilitzen la mateixa base en l'arribada que en la sortida i perquè la imatge del tercer vector, que coincideix amb el vector llum, sempre serà (0,0,0).
La matriu A3 és la del pla1 (pla paret) i la base de sortida i d'arribada és {(1,0,0),(0,0,1),(2,4,3)}.
La matriu A4 és la del pla2 (pla terra) i la base de sortida i d'arribada és {(1,0,0),(0,1,0),(2,4,3)}.
Com quedarien ara les matrius de canvi de base?
> C1:=matrix(3,3,[1,0,2,0,0,4,0,1,3]);
[1 0 2]
[ ]
C1 := [0 0 4]
[ ]
[0 1 3]
> B1:=inverse(matrix(3,3,[1,0,2,0,0,4,0,1,3]));
[ -1 ]
[1 -- 0]
[ 2 ]
[ ]
[ -3 ]
B1 := [0 -- 1]
[ 4 ]
[ ]
[ 1 ]
[0 - 0]
[ 4 ]
> C2:=matrix(3,3,[1,0,2,0,1,4,0,0,3]);
[1 0 2]
[ ]
C2 := [0 1 4]
[ ]
[0 0 3]
> B2:=inverse(matrix(3,3,[1,0,2,0,1,4,0,0,3]));
[ -2]
[1 0 --]
[ 3 ]
[ ]
[ -4]
B2 := [0 1 --]
[ 3 ]
[ ]
[ 1]
[0 0 -]
[ 3]