Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Determinants - Linear Algebra - Exam, Exams of Linear Algebra

Mody University of Science and TechnologyLinear Algebra

This is the Exam of Linear Algebra which includes Encouraged, Vectors, System, Method, Factorization, Square Matrices, Throughout, Invertible, Symmetric etc. Key important points are: Determinants, Properties, Obtained, Interchanging, Invertible, Factorization, Equation, Formula, Invertible, Using Pivots

Typology: Exams

2012/2013

Uploaded on 02/27/2013

selvi_pr43
selvi_pr43 🇮🇳

4.7

(3)

66 documents

1 / 6

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Math 205 Section B
Test 2 (50 points)
Name:
•Check that you have 6 questions on three pages.
•Show all your work to receive full credit for a problem.
1. (10 points) Let Aand Bbe 4×4 matrices, with det A=−10 and det B= 6. Use properties
of determinants to compute:
(a) det A2BT
(b) det 2B
(c) det Cwhere Cis obtained from Aby interchanging rows 2 and 4
(d) det (B2)−1if B2is invertible. Otherwise, explain why B2is not invertible.
pf3
pf4
pf5

Partial preview of the text

Download Determinants - Linear Algebra - Exam and more Exams Linear Algebra in PDF only on Docsity!

Math 205 Section B

Test 2 (50 points)

Name:

  • Check that you have 6 questions on three pages.
  • Show all your work to receive full credit for a problem.
  1. (10 points) Let A and B be 4 × 4 matrices, with det A = −10 and det B = 6. Use properties of determinants to compute: (a) det A^2 BT

(b) det 2B

(c) det C where C is obtained from A by interchanging rows 2 and 4

(d) det (B^2 )−^1 if B^2 is invertible. Otherwise, explain why B^2 is not invertible.

  1. (8 points) Let A =

[ 2 4 − 2

]

(a) Find an LU factorization of A.

(b) Use the LU factorization in part (a) to solve the equation A~x =

[ 1

]

  1. (8 points) Supose a 5 × 5 matrix A is invertible. Explain (using pivots) why the columns of A are linearly independent. (If you find it helpful, you may use the following steps in your explanation.)

Since A is invertible, A reduces to.

So the number of pivots in A is

Use this to explain why the columns of A are linearly independent.

  1. (8 points) Determine if each of the following sets is a subspace of the appropriate vector space.

(a) Let W =

a b a + b

 (^) : a, b are real numbers.

. Is^ W^ a subspace of^ R

(^3)? Explain.

(b) Let W be the set of all polynomials of the form p(t) = t + a where a is a real number. Is W a subspace of P 1? Explain. (P 1 is the set of all polynomials of degree atmost one.)