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

/* code_begins */

{{{
q1=matrix([2/3],[2/3],[-1/3]])
q2=matrix([[-1/3],[2/3],[2/3]])
q1.transpose()*q2==0                               /* checking the condition for orthonormal vectors*/
Q=matrix([[2/3,-1/3],[2/3,2/3],[-1/3,2/3]])
Q.transpose()
Q.transpose()*Q                                    /* this results in an identity matrix*/
Q1=Q*Q.transpose()
Q1
A=Q*(Q.transpose()*Q).inverse()*(Q.transpose())    /* calculating the projection matrix over the two vectors q1,q2*/
A==Q1                                               /*checking if Q1 itself is the projection matrix*/
}}}

/* code_ends */


 * '''Solution by''': 
   * <deepthi>, <student>, <SNIST>
   * <manisha>, <student>,<SNIST>