• Book	Linear Algebra
  Author	Gilbert Strang
  Edition

code_begins

(i)
a=var('a')
b=var('b')
c=var('c')
A=matrix([[0,a,0],[0,0,b],[c,0,0]])
A.swap_rows(2,0)
A.swap_rows(1,2)
print A
print A[0,0]*A[1,1]*A[2,2]
(ii)
a=var('a')
b=var('b')
c=var('c')
d=var('d')
B=matrix([[0,a,0,0],[0,0,b,0],[0,0,0,c],[d,0,0,0]])
B.swap_rows(0,3)
B.swap_rows(1,3)
B.swap_rows(2,3)
print B
print B[0,0]*B[1,1]*B[2,2]*B[3,3]
(iii)
a=var('a')
b=var('b')
c=var('c')
C=matrix([[a,a,a],[a,b,b],[a,b,c]])
c=C.echelon_form()
print c[0,0]*c[1,1]*c[2,2]

code_ends

• Solution by:

• Swethakumari G, student,SNIST
• Radha Bhukya, student, SNIST
• Usha Rani,student, SNIST