||'''Book'''|| Linear Algebra ||
 ||'''Author'''|| Gilbert Strang ||
 ||'''Edition'''||  ||

/* code_begins */

{{{
A=A0=matrix([[4,0,0],[0,5,0]])
A
r=m=A.rank()
r
C=(A.transpose()*((A*A.transpose()).inverse()))
C
var('b13,b23')
B=matrix([[1/4,0,b13],[0,1/5,b23]])
B
B*A.transpose()
T1=matrix([[4,0],[0,5],[0,0]])
T1
A
Arank1=matrix([[2,1,1],[4,2,2],[8,4,4],[-2,-1,-1]])
Arank1.rank()
u=matrix([[1],[2],[4],[-1]])
vt=matrix([2,1,1])
Res=u*vt
Res
Res==Arank1
}}}

/* code_ends */

 * '''Solution by''': 
   * <T.R.N.Karthik>, <Student>, <Gitam University>