Symbolic Matrices

A:=matrix [[x,y],[z,w]]

(1)

A+1

(2)

A+2

(3)

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N:=matrix[[0],[0]]

(4)

L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

(5)

A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

(6)

v:=matrix[[v11],[v12]]

(7)

C:=A*v-L(1,1)*v

(8)

solve(C(1,1)=0,v11)

(9)

solve(C(2,1)=0,v12)

(10)

V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

(11)

Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

(12)

W:=(V(1,1)*V(2,2) - V(1,2)*V(2,1))

(13)

N:=matrix[[0],[0]]

(14)

L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

(15)

A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

(16)

v:=matrix[[v11],[v12]]

(17)

C:=A*v-L(1,1)*v

(18)

solve(C(1,1)=0,v11)

(19)

solve(C(2,1)=0,v12)

(20)

V:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

(21)

Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

(22)

V(1,1)*V(2,2)

(23)

V(1,2)*V(2,1)

(24)

N:=matrix[[0],[0]]

(25)

L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

(26)

A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

(27)

v:=matrix[[v11],[v12]]

(28)

C:=A*v-L(1,1)*v

(29)

solve(C(1,1)=0,v11)

(30)

solve(C(2,1)=0,v12)

(31)

T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

(32)

a:=sqrt(T(1,1)^2+T(2,1)^2)

(33)

b=sqrt(T(1,2)^2+T(2,2)^2)

(34)

Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

(35)

V(1,1)*V(2,2)

(36)

V(1,2)*V(2,1)

(37)

N:=matrix[[0],[0]]

(38)

L:=[[sqrt(-1)*sin(x)+cos(x)],[-sqrt(-1)*sin(x)+cos(x)]]

(39)

A:=matrix[[cos(x),-sin(x)],[sin(x),cos(x)]]

(40)

v:=matrix[[v11],[v12]]

(41)

C:=A*v-L(1,1)*v

(42)

solve(C(1,1)=0,v11)

(43)

solve(C(2,1)=0,v12)

(44)

T:=matrix[[1/sqrt(-1),1],[1,-1/sqrt(-1)]]

(45)

sqrt(T(1,1)^2+T(2,1)^2)

(46)

sqrt(T(1,2)^2+T(2,2)^2)

(47)

Z:=matrix[[V(2,2),-V(1,2)],[-V(2,1),V(1,1)]]

(48)

V(1,1)*V(2,2)

(49)

V(1,2)*V(2,1)

(50)

)clear all

   All user variables and function definitions have been cleared.
B := %i*sqrt(a^2 + b^2 + c^2)

(51)

A := matrix[ [B, c, -b], [-c, B, a], [b, -a, B] ]

(52)

rowEchelon(A)

(53)

B := -%i*sqrt(a^2 + b^2 + c^2)

(54)

A := matrix[ [B, c, -b], [-c, B, a], [b, -a, B] ]

(55)

rowEchelon(A)

(56)