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

/* code_begins */

{{{
A=matrix([[4,2],[1,3]])
print "Given matrix A as:\n",A
print "Finding the inverse of A using A.inverse() function\n",A.inverse()
print "Let I be an Identity matrix of dimensions 2*2"
I=matrix([[1,0],[0,1]])
print "I=\n",I
print "Let k be any variable" 
var('k')
k*I
print "Let T be a matrix given by T=A-k*I"
T=A-k*I
print "T=\n",T
print "Given to find the values of k for which matrix T is singular"
print "For any matrix to be singular,its determinant should be equal to zero"
print "Determinant of T is given as :",T.det()
print "Let determinant of T be p(k)"
p(k)=T.det()
print "p(k)=",p(k)
print "Solving p(k) using solve() function,we can obtain the values for k"
print "Thus given matrix T=A-k*I can be singular iff \n "
solve((k - 4)*(k - 3) - 2,k)

Result:

Given matrix A as:
[4 2]
[1 3]
Finding the inverse of A using A.inverse() function
[ 3/10  -1/5]
[-1/10   2/5]
Let I be an Identity matrix of dimensions 2*2
I=
[1 0]
[0 1]
Let k be any variable
Let T be a matrix given by T=A-k*I
T=
[-k + 4      2]
[     1 -k + 3]
Given to find the values of k for which matrix T is singular
For any matrix to be singular,its determinant should be equal to zero
Determinant of T is given as : (k - 4)*(k - 3) - 2
Let determinant of T be p(k)
p(k)= (k - 4)*(k - 3) - 2
Solving p(k) using solve() function,we can obtain the values for k
Thus given matrix T=A-k*I can be singular iff 
 
[k == 5, k == 2]
}}}

/* code_ends */

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