{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

assig3_2011

# assig3_2011 - Express the vector[2 1 0 as a linear...

This preview shows pages 1–2. Sign up to view the full content.

Math 152, Spring 2011 Assignment #3 Notes: Each question is worth 5 marks. Due in class: Monday, January 24 for MWF sections; Tuesday, January 25 for TTh sections. Solutions will be posted Tuesday, January 25 in the afternoon. No late assignments will be accepted. 1. Consider the vectors a = [2 , 0 , - 1] and b = [1 , 3 , 1]. (a) (2 marks) What is the angle between a and b ? Remember that it is better to use the dot product to determine angles between two vectors. (b) (3 marks) What is the area of the parallelogram with a and b as sides? 2. Consider the vectors a = [2 , 0 , 3], b = [ - 1 , 2 , 2] and c = [2 , 0 , 0]. (a) (4 marks) Determine whether these vectors are linearly indepen- dent. ( Hint : use a matrix with row vectors a , b and c .) (b) (1 mark) Can any vector x with three components be expressed as a linear combination of a , b and c ? Justify briefly. 3. (5 marks) Consider the vectors a , b and c given in problem 2 above.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Express the vector [2, 1, 0] as a linear combination of a , b and c . 4. (5 marks) Let a = [-7, -1, 0] and b = [-2, 0, 1]. Find all vectors c such that the vectors a , b and c are linearly dependent (that is they all lie on the same plane). 5. Consider the three planes P 1 , P 2 and P 3 de²ned by: P 1 : x + 2 y-z = 5 P 2 : c x + y + z =-2 P 3 : d x-2 y + h z = 11 where c , d and h are constants. (a) (2 marks) Find all constants c , d and h such that these three planes intersect in a single point. (Do not fnd the intersection point.) (b) (2 marks) For which values o± d and h are the two planes P 1 and P 3 parallel? ( Hint : use the vectors normal to these planes.) (c) (1 mark) For what value o± c are the two planes P 1 and P 2 parallel?...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern