Exercise #18, 2.4 (Anton-Rorres: Elementary Linear Algebra, 8E)

(12:07) gp > A = [1,4,1;4,-1,2;2,2,-3]
%46 = 
[1 4 1]

[4 -1 2]

[2 2 -3]

(12:07) gp > matdet(A)
%47 = 73

(12:07) gp > A1=[6,4,1;-1,-1,2;-20,2,-3]
%48 = 
[6 4 1]

[-1 -1 2]

[-20 2 -3]

(12:08) gp > matdet(A1)
%49 = -200


(12:08) gp > A2=[1,6,1;4,-1,2;2,-20,-3]
%50 = 
[1 6 1]

[4 -1 2]

[2 -20 -3]

(12:08) gp > matdet(A2)
%51 = 61

(12:08) gp > A3=[1,4,6;4,-1,-1;2,2,-20]
%52 = 
[1 4 6]

[4 -1 -1]

[2 2 -20]

(12:09) gp > matdet(A3)
%53 = 394

Then by Cramer's Rule the solutions are:

(12:15) gp > x1 = matdet(A1)/matdet(A)
%57 = -200/73
(12:15) gp > x2=matdet(A2)/matdet(A)
%58 = 61/73
(12:15) gp > x3=matdet(A3)/matdet(A)
%59 = 394/73
(12:16) gp > 


Check with matinverseimage:


(12:09) gp > A
%54 = 
[1 4 1]

[4 -1 2]

[2 2 -3]

(12:10) gp > b = [6;-1;-20]
%55 = 
[6]

[-1]

[20]

(12:10) gp > matinverseimage(A,b)
%56 = 
[-200/73]

[61/73]

[394/73]