Determine the Set of Vectors Exam Practice

write the steps clearly especially for the question 4.

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1. (3 pts) Determine whether the set of vectors
21 21 2 2
3′ 3’33’3′ )
(-3′})(313):63 } is orthogonal. Is it orthonormal? Explain.
(Hint: why would I ask
2. (2 pts) Find the inverse of A=
cos -sine
sine cose
you to find this on this particular groupwork?)
3. (9 pts) Let B= 1-3
Bee
[4]
a. Use Gram Schmidt to create an orthonormal basis using -3 as the
10
first vector .
b. Use your basis to create an orthogonal matrix A.
c. Find the inverse of the matrix you created in part b.
[1
d. Let u= 2 find magnitude of ū and magnitude of Aŭ. What do you
|-2
notice?
4. (4 pts) True or False (give reasons for your answers)
a. Every orthogonal set of vectors is linearly independent.
b. Every non-trivial subspace i.e. ignore the subspace consisting of only
the zero vector) of Rhas an orthogonal basis.
c. projw() is orthogonal to every vector in W.
d. If det A=+1 then A is orthogonal.