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Quiz 7 Solutions - Applied Linear Algebra | MATH 310, Quizzes of Linear Algebra

University of Illinois - ChicagoLinear Algebra

Material Type: Quiz; Class: Applied Linear Algebra; Subject: Mathematics; University: University of Illinois - Chicago;

Typology: Quizzes

2011/2012

Uploaded on 05/03/2012

billyking100
billyking100 🇺🇸

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Math 310, 1pm
Quiz 7 solutions: 5.1
Find the angle between ~x = (3,4)Tand ~y = (−1,7)T. If applicable, give an exact answer (in
terms of π).
formula: cos θ=~x T~y
k~xkk~yk
~x T~y =−3 + 28 = 25
k~xk=√32+ 42=√25 = 5
k~yk=p(−1)2+ 72=√50 = 5√2
cos θ=25
25√2=1
√2⇒θ= cos−11
√2⇒θ=π
4
1

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Math 310, 1pm Quiz 7 solutions: 5.

Find the angle between ~x = (3, 4)T^ and ~y = (− 1 , 7)T^. If applicable, give an exact answer (in

terms of π).

formula: cos θ =

~x T^ ~y

‖~x‖ ‖~y‖

~x T^ ~y = −3 + 28 = 25

‖~x‖ =

32 + 4^2 =

‖~y‖ =

(−1)^2 + 7^2 =

cos θ =

⇒ θ = cos

− 1

⇒ θ =

π

4