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This is the Quiz of Linear Algebra which includes Zero Vector, Linearly Dependent, Statement, Vector, Linear Combination, Expressed, Trivial Solution, Inspection, Dependent, Theorem etc. Key important points are: Unit Vector, Direction, Orthogonal Basis, Linear Algebra, Techniques, Formulas Developed, Orthogonal Bases, Vectors Horizontally, Familar Ground, Vectors Vertically
Typology: Exercises
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Math 205B&C 03/27/09 Quiz 07 page 1 Name 8am 1:10 pm
, v 2 =
(^) and v 3 =
x y
; let s =
1a. Explain why v 1 ⊥ v 2.
1b. Find a unit vector in the direction of v 2.
1c. Find x and y which make B = {v 1 , v 2 , v 3 } an orthogonal basis of R^3. (Use good linear algebra techniques; your answer will involve a RREF).
1d. Use the formulas developed in class for orthogonal bases to find α 2 for which s = α 1 v 1 +α 2 v 2 +α 3 v 3. (You do not have to find α 1 and α 3 .)
then RREF(A) is^ R^ =
Find a basis for each of the
following. Write vectors horizontally where appropriate.
2a. Col(A) 2b. Col(R)
2c. Row(A) 2d. Row(R)
2e. Express r 3 (ie, row 3) of A as a linear combination r 3 = xr 1 + yr 2 + zr 4. of the other three rows of A. (Hint: you will be on familar ground if you write the vectors vertically to solve the problem; find x y and z. Or explain why there are no such scalars. Use good linear algebra methods)