Sample/practice exam 2020, questions and answers PDF

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Math225

Exam 2

Summer 2016-2017

Student Name : ________________________________ Student I.D

: ________________________________

Lebanese International University School of Arts and Sciences

Course Name

: Linear Algebra with Applications

Course Code

: Math 225

Exam

: Exam 2

Section

:

Date

: 20 / 7 / 2017

Time

: 2:00---3:15

Semester

: Summer

Year

: 2016 – 2017

Instructor

:

Exam Weight

: 25 %

Auditorium

:

Campus

: All campuses

Instructions

Problem #

Grade

Exercise 1

/15

Exercise 2

/25

 Read each question carefully before answering

Exercise 3

/30

 Answer questions that you are confident about it first.

Exercise 4

/30

Total

/100

 Time allowed: 75 minutes  Cheating in any way will result in F grade

 This exam consists of 10 pages including this page

1 LIU

Math225

Exam 2

Summer 2016-2017

Exercise 1 (15 marks) Answer by true or false (with justification)

1)

(

)

2) 3) The coordinate matrix of 4) The functions

( ) 5) Let subspace of .

is a subspace of .

is a basis for ( )

( ) in relative to the basis and

form a linearly independent set in .

be a subspace of . Then

2 LIU

 (4,0),(0,3) is [ ]

is a two-dimensional

[

]

Math225

Exam 2

3 LIU

Summer 2016-2017

Math225

Exam 2

Exercise 2 (25 marks) Let

()

1) Show that forms a subspace of 2) Find a basis of and deduce its dimension.

4 LIU

Summer 2016-2017

Math225

Exam 2

5 LIU

Summer 2016-2017

Math225

Exam 2

Exercise 3 (30 marks)

Let

[

)

] and ( 1) Solve the equation and deduce a basis for , the null space of . 2) Find a basis for the row space of and deduce rank( ). 3) Find the nullity of by two different methods.

6 LIU

Summer 2016-2017

Math225

Exam 2

7 LIU

Summer 2016-2017

Math225

Exam 2

Summer 2016-2017

Exercise 4 (30 marks) (Parts A, B and C are independent)

)

Let ( Part A

If possible, write the fourth column of matrix as a linear combination of the first two columns.

Part B Let

(

)

1) Show that

(

) and

Let

and

(

)

forms a basis for

2) Find the coordinates of Part C

(

)

(

(

) and

Find the values of , for which the set

) with respect to the basis . (

)

is linearly independent.

8 LIU

Math225

Exam 2

9 LIU

Summer 2016-2017

Math225

Exam 2

Extra Sheet

10 LIU

Summer 2016-2017...