write the steps clearly especially for the question 4.

……………………….

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.