Question Details

[answered] Ministry of Higher Education Kingdom of Saudi Arabia CSTS S


please Help solving this assignment in Linear Algebra as soon as possible. THANKS?


Ministry of Higher Education

 

Kingdom of Saudi Arabia CSTS

 

SEU, KSA Linear Algebra (Math 251)

 

Level IV, Assignment 3

 

(Fall, 2016) 1. State whether the following statements are true or false: [6] (a) If 2, 3 and 4 are eigen values of a matrix A, then det(A) = 9.

 

(a)

 

(b) (1,-1,2) is the real part of the complex vector (1 + i, ?1 + i, i, 2).

 

(b)

 

(c) The inner product of a nonzero vector with itself is always a positive real number.

 

(c)

 

(d) If u = (1, ?1), v = (?2, 2) and k = 4, then < ku, v >= 16.

 

(d)

 

(e) If determinant of a matrix is 1 or -1, then the matrix is orthogonal.

 

(e)

 

(f) The rows and columns of an orthogonal matrix are orthonormal.

 

(f) Page 1 of 3 Last Date: 14 Dec, 2016 Math 251 Department of Mathematics 2. Select one of the alternatives from the following questions as your answer.

 



 



 

3 1

 

(a) The characteristic equation of the matrix A =

 

is

 

2 4

 

A. ?2 ? 7? ? 10 = 0

 

B. ?2 + 7? ? 10 = 0

 

C. ?2 ? 7? + 10 = 0

 

D. ?2 + 7? + 10 = 0 1 ?1 2

 

1 , are

 

(b) The eigenvalues of the matrix A3 , where A = 0 4

 

0 0 ?3

 

A. {1, 4, ?3}

 

B. {1, 12, ?9}

 

C. {1, 64, 27}

 

D. {1, 64, ?27}

 

(c) Which of the following sets of vectors are orthogonal with respect to the Euclidean

 

inner product on R2 :

 

A.

 

B.

 

C.

 

D. (1,2), (-2,1)

 

(3,4),(2,6)

 

(6,9),(5,2)

 

(0,4), (0,6) (d) If angle between vectors u and v is zero such that kuk = 4, kvk = 6, then < u, v >=

 

A. 10

 

B. 24

 

?

 

C. 24

 

?

 

D. 10

 

(e) If 3x21 +2x22 ?4x23 ?2x1 x2 +6x1 x3 ?4x2 x3 be the quadratic form, then the associated

 

symmetric matrix will be 3 1

 

3

 

A. 1 2 ?2 3 ?2 ?4 3 ?1 ?3

 

B. ?1 2 ?2 ?3 ?2 ?4 3 ?1 3

 

2 C. ?1 2

 

3

 

2 ?4 Page 2 of 3 Last Date: 14 Dec, 2016 [6] Math 251 Department of Mathematics 3 ?1 3

 

D. ?1 2 ?2 3 ?2 ?4 3

 

i + 2 2 + 6i

 

?1 2i ? 1 is Hermitian?

 

(f) For which value of a and b, the matrix a

 

2 ? 6i

 

b

 

1

 

A. a = i ? 2, b = ?2i ? 1

 

B. a = ?i + 2, b = 2i + 1

 

C. a = ?i + 2, b = ?2i ? 1

 

D. a = i ? 2, b = 2i + 1

 



 



 

5 ?2

 

3. Find all the eigenvalues and the corresponding eigenvectors of the matrix A =

 

.

 

3 0

 



 



 

1 + 3i

 

2

 

4. For the matrix A =

 

Find A, Re(A), Im(A), T r(A) and det(A).

 

3+i 4?i

 



 



 



 



 

9 4

 

2 ?2

 

5. Find the value of k, for which the matrices U =

 

and V =

 

are

 

2 6

 

k 4

 

orthogonal in the vector space M2?2 with usual inner product on M2?2 .

 

6. Find 1 2

 

2 the least squares

 

solution

 

of the system of linear equation AX = B, where A = ?3

 

?2

 

1 , B = 2 .

 

1

 

0 1

 

1?i ?

 

? ? 3 7. Show that the matrix A = 1 +3i is unitary.

 

1

 

?

 

?

 

3

 

3 2 3

 

6 7 7

 

7 3

 

6

 

2 is orthogonal and find A?1 .

 

8. Show that matrix A = ? 7 6 27 73 ?

 

7 7

 

7 Page 3 of 3 End of Assignment. [4]

 

[2]

 

[2] [4] [3] [3]

 


Solution details:
STATUS
Answered
QUALITY
Approved
ANSWER RATING

This question was answered on: Sep 18, 2020

PRICE: $15

Solution~0001013904.zip (25.37 KB)

Buy this answer for only: $15

This attachment is locked

We have a ready expert answer for this paper which you can use for in-depth understanding, research editing or paraphrasing. You can buy it or order for a fresh, original and plagiarism-free copy from our tutoring website www.aceyourhomework.com (Deadline assured. Flexible pricing. TurnItIn Report provided)

Pay using PayPal (No PayPal account Required) or your credit card . All your purchases are securely protected by .
SiteLock

About this Question

STATUS

Answered

QUALITY

Approved

DATE ANSWERED

Sep 18, 2020

EXPERT

Tutor

ANSWER RATING

GET INSTANT HELP/h4>

We have top-notch tutors who can do your essay/homework for you at a reasonable cost and then you can simply use that essay as a template to build your own arguments.

You can also use these solutions:

  • As a reference for in-depth understanding of the subject.
  • As a source of ideas / reasoning for your own research (if properly referenced)
  • For editing and paraphrasing (check your institution's definition of plagiarism and recommended paraphrase).
This we believe is a better way of understanding a problem and makes use of the efficiency of time of the student.

NEW ASSIGNMENT HELP?

Order New Solution. Quick Turnaround

Click on the button below in order to Order for a New, Original and High-Quality Essay Solutions. New orders are original solutions and precise to your writing instruction requirements. Place a New Order using the button below.

WE GUARANTEE, THAT YOUR PAPER WILL BE WRITTEN FROM SCRATCH AND WITHIN YOUR SET DEADLINE.

Order Now