MTH 1230 - Spring 2001- Exam 3

Problem 1

<<LinearAlgebra`Orthogonalization`

{w1, w2, w3} = GramSchmidt[{{1,1,1,1}, {1,-1,1,-1}, {0,0,1,1}}]

Problem 2

A={{-3,4},{9,-12}};

NullSpace[A]

NullSpace[%]

NullSpace[Transpose[A]]

NullSpace[%]

Problem 3

v1={a,a,a}; v2={0,b,c};

{v1, v2} /. Solve[{v1 . v1 == 1, v1 . v2 == 0, v2 . v2 == 1}, {a, b, c}]

Problem 5

A={{1,1},{0,1},{1,0}};  b={-1,5,3};

Transpose[A].A

Inverse[Transpose[A].A]

P=Inverse[Transpose[A].A].Transpose[A]

PseudoInverse[A]

x=P.b

A.P

A.P.b