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Cs606 Assignment 3 Solution 2016 Tax

MTH501 assignment no 3 (due date 8 January 2017)


For a nonempty subset  of a vector space, under the inherited operations, the following are equivalent statements
  1.  is a subspace of that vector space
  2.  is closed under linear combinations of pairs of vectors: for any vectors  and scalars  the vector  is in 
  3.  is closed under linear combinations of any number of vectors: for any vectors  and scalars  the vector  is in .
Anyone have idea about it, please leave comment and  am trying  to solve

Idea About Problem no 2

S = {

 , 

}

Of vectors in the vector space R3, find a basis for span S.

The set S = {v1v2} of vectors in R3 is linearly independent if the only solution of

  c1v1 + c2v2 = 0

is c1, c2 = 0.

In this case, the set S forms a basis for span S.

Otherwise (i.e., if a solution with at least some nonzero values exists), S is linearly dependent.

If this is the case, a subset of S can be found that forms a basis for span S.

With our vectors v1v2, (*) becomes:

c1

 + 

c2

 = 

Rearranging the left hand side yields

0 c1 +1 c2

4 c1 +2 c2

1 c1 +3 c2

 = 

The matrix equation above is equivalent to the following homogeneous system of equations

0 c1

 +1 c2

=

0

4 c1

 +2 c2

=

0

1 c1

 +3 c2

=

0

We now transform the coefficient matrix of the homogeneous system above to the reduced row echelon form to determine whether the system has
  • the trivial solution only (meaning that S is linearly independent), or
  • the trivial solution as well as nontrivial ones (S is linearly dependent).

 0 

 1 

 4 

 2 

 1 

 3 

can be transformed by a sequence of elementary row operations to the matrix

 1 

 0 

 0 

 1 

 0 

 0 

The reduced row echelon form of the coefficient matrix of the homogeneous system is

 1 

 0 

 0 

 1 

 0 

 0 

which corresponds to the system

1 c1

=

0

1 c2

=

0

0

=

0

Since each column contains a leading entry (highlighted in yellow), then the system has only the trivial solution, so that the only solution of  is c1, c2 = 0.
Therefore the set S = {v1v2} is linearly independent.

Consequently, the set S forms a basis for span S and many set of solution.

2005 Connecticut Code - Sec. 53a-139. Forgery in the second degree: Class D felony.

Sec. 53a-139. Forgery in the second degree: Class D felony. (a) A person is guilty of forgery in the second degree when, with intent to defraud, deceive or injure another, he falsely makes, completes or alters a written instrument or issues or possesses any written instrument which he knows to be forged, which is or purports to be, or which is calculated to become or represent if completed: (1) A deed, will, codicil, contract, assignment, commercial instrument or other instrument which does or may evidence, create, transfer, terminate or otherwise affect a legal right, interest, obligation or status; or (2) a public record or an instrument filed or required or authorized by law to be filed in or with a public office or public servant; or (3) a written instrument officially issued or created by a public office, public servant or governmental instrumentality; or (4) a prescription of a duly licensed physician or other person authorized to issue the same for any drug or any instrument or device used in the taking or administering of drugs for which a prescription is required by law.

(b) "Drugs" as used in this section includes all drugs except controlled drugs as defined in section 21a-240.

(c) Forgery in the second degree is a class D felony.

(1969, P.A. 828, S. 141; 1971, P.A. 871, S. 38; P.A. 76-292, S. 2.)

History: 1971 act removed exception re narcotic drugs in Subsec. (b); P.A. 76-292 made second degree forgery a Class D felony rather than a Class A misdemeanor.

Cited. 201 C. 125, 126. Cited. 207 C. 555, 560. Defendant may be found guilty of forgery in the second degree if the state establishes that defendant, with intent to deceive another, falsely made, possessed or altered a written instrument that he or she knew to be forged. 252 C. 229.

Cited. 8 CA 342, 343. Cited. 11 CA 161, 162, 166. Cited. 28 CA 521, 523, 530, 532. Cited. 37 CA 72, 80. Cited. 42 CA 790. Forgery statute, Sec. 53a-138 et seq. Cited. 47 CA 1.

Cited. 34 CS 606, 610.

Subsec. (a):

Subdiv. (1). Cited. 169 C. 581. Subdiv. (2) cited. 195 C. 421, 423. Subdiv. (2) cited. 198 C. 68, 69. Subdiv. (1) cited. Id., 158, 160. Subdiv. (2) cited. 199 C. 146, 148. Cited. 201 C. 125, 149, 151, 153. Subdiv. (2) cited. Id., 125, 149, 150. Subdiv. (1) cited. 207 C. 555, 556, 559. Subdiv. (1) cited. 235 C. 469, 470.

Subdiv. (2) cited. 5 CA 473, 474. Subdiv. (1) cited. 14 CA 1, 2. Subdiv. (2) cited. 24 CA 493, 494. Subdiv. (3) cited. Id. Cited. 28 CA 521, 523. Subdiv. (1) cited. 37 CA 72, 78. Subdiv. (1) cited. 42 CA 790. Subdiv. (2) cited. 47 CA 1.

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