Week 4 questions.docx

week_4_questions.docx

Unformatted Attachment Preview

Don't use plagiarized sources. Get Your Custom Essay on

Linear Algebra questions

Just from $13/Page

1: Given a linear transformation

T : R2 ? R2

defined by

? ? x1 ? ? ? 2 x1 – x2 ?

T ?? ? ? ?? = ?

?

x

x

+

x

?

?

?

1

2 ?

? 2 ?

a) Find the matrix of this linear transformation with respect to the

standard ordered bases B to B, where B=

? ?1 ? ? 0? ?

? ? ?, ? ? ?

? ? 0? ?1 ? ?

b) Find the matrix of this linear transformation with respect to the

ordered

? ?1? ? 1 ? ?

bases C to C, where C= ?

?1? , ? – 1? ?

?? ? ? ? ?

2. For the linear transformation

(

)

D : P2 ? P2 defined by

D a0 + a1 x + a2 x 2 = a1 + 2a2 x

a) Find the matrix of this linear transformation with respect to the

standard ordered bases B to B, where B=

?1, x, x 2 ?

b) Find the matrix of this linear transformation with respect to the

ordered bases C to C, where C=

?1 – x,1 + x, x 2 ?

T : R 2 ? P1 be the linear transformation defined by

? ?1 ? ? 0? ?

? 2 1?

with respect to the bases ?

A= ?

, ? ? ? and ?1 – x,1 + x?

?

?

?

?1 1?

? ? 0? ?1 ? ?

3. Let

of

R

2

and

?? 3 ??

P1 respectively. Find T ?? ? ? ?? .

? ? – 2? ?

Solve this problem using this example: 2.1 Example Consider this matrix.

1 2

H =(3 4)

5 6

It is 3×2 so any map that it defines must carry a dimension 2 domain to a

dimension 3 codomain. We can choose the domain and codomain to be

R2 and?2 , with these bases

1

1

? = <( ) , ( )> D =

1

-1

Then let h: R2 -> ?2 be the function defined by H. We will compute the image

under h of this member of the domain.

-3

(?? = ( ))

2

The computation is straightforward.

-11/2

1 2 -1/2

???? (h(??)) = H · ???? (??) =(3 4) (

) = (-23/2)

-5/2

-35/2

5 6

From its representation,

computation of ?

??? is routine (-11/2)(? 2 )-(23/2)(? 2 + ?) – (35/2)(? 2 + x + 1) =

(-69/2)? 2 – (58/2)x – (35/2).

6. Use the method of example 4.9 to find the inverse of the matrix

? 2 1 2?

? 1 1 3?

?

?

?? 2 1 1 ??

4.9 Example This one happens to start with a row swap.

0

(1

1

3 -1 1 0

0

1 |0 1

-1 0 0 0

0

1 0

1 0

?1 < -> ?2 (0 3 -1|1

0) ?????????????????????????

1

1 -1 0 0

1

???????????????????

-?1 + ?3 (0

0

0

1 0

3 -1|1

-1 -1 0

1 0

0 0)

-1 1

?

1 0

? (0 1

0 0

0 1/4

0| 1/4

1 -1/4

1/4 3/4

1/4 -1/4)

3/4 -3/4

1 0

0 0)

0 1

…

Purchase answer to see full

attachment

Basic features

- Free title page and bibliography
- Unlimited revisions
- Plagiarism-free guarantee
- Money-back guarantee
- 24/7 support

On-demand options

- Writer’s samples
- Part-by-part delivery
- Overnight delivery
- Copies of used sources
- Expert Proofreading

Paper format

- 275 words per page
- 12 pt Arial/Times New Roman
- Double line spacing
- Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Delivering a high-quality product at a reasonable price is not enough anymore.

That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read moreEach paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read moreThanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read moreYour email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read moreBy sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more