**MA8352 LAPDE Question Papers**

Anna University Regulation 2017 ECE **MA8352 **LAPDE** Question Papers for previous years** are provided below. **Previous Year Question Papers for **ECE **3rd SEM MA8352 Linear Algebra and Partial Differential Equations, Engineering** are listed down for students to make perfect utilization and score maximum marks with our study materials.

### Anna University Regulation 2017 (ECE) 3rd SEM MA8352 LAPDE – Linear Algebra and Partial Differential Equations question paper

1.Define Vector Space

2.Define Subspace of a vector space

3.State the necessary and sufficient condition for a subset of a vector space to be subspace

4.Do the polynomials ?3−2?2+1,4?2−?+3 and 3?−2 generate ?3(?)? Justify your answer.

5.Is {(1,4,−6),(1,5,8),(2,1,1),(0,1,0)} is a linearly independent subset of ?3 ? Justify your answer

6.The vectors ?1=(2,−3,1),?2=(1,4,−2),?3=(−8,12,−4),?4=(1,37,−17) and ?5=(−3,−5,8) generate ?3. Find a subset of the set {?1,?2,?3,?4,?5} that is a basis for ?3

7.Let ? and ? be distinct vectors of a vector space ?. Show that if {?,?} is a basis for ? and ? and ? are non-zero scalars, then both {?+?,??} and {??,??} are also bases for ?.

8.Write the vectors ?=(1,−2,5) as a linear combination of the vectors ?=(1,1,1),?=(1,2,3) and ?=(2,−1,1)

9.Show that the set of all polynomials in one variable over a field F of degree less than or equal to n is a subspace of the vector space of all polynomials over F

10.Determine whether the set W={(?1,?2,?3)??3:?1+2?2-3?3=1} is a subspace of ?3 under the operations of addition and scalar multiplication

11.Determine whether ?=(4,−7,3) can be written as a linear combination of ?1=(1,2,0) and ?2=(3,1,1) in ?3

12.For which value of k will the vector ?=(1,−2,?) in ?3 be a linear combination of the vectors ?=(3,0,−2) and ?=(2,−1,5)?

13.Determine whether the set ?1={(?1,?2,?3)∈?3∶ ?1=?3+2} is a subspace of ?3 under the operations of addition and scalar multiplication defined on ?3

14.Point out whether the set ?1={(?1,?2,?3)∈?3∶ ?1−4?2−?3=0} is a subspace of ?3 under the operations of addition and scalar multiplication defined on ?3

15.Check whether 2?3−2?2+12?−6 is a linear combination of?3−2?2−5?−3 and 3?3−5?2−4?−9

16.Point out whether ?=(3,4,1) can be written as a linear combination of ?1=(1,−2,1) and ?2=(−2,−1,1) in ?3

17.Point out whether the given vector is in the span of ?∶

i) (2,−1,1,−3),?={(1,0,1,−1),(0,1,1,1)}

ii) 2?3−?2+?+3,?={?3+?2+?+1,?2+?+1,?+1}

18.Show that the vectors {(1,1,0),(1,0,1) and (0,1,1)} genarate ?3

19.Check whether the vectors (i) {?3+2?2,−?2+3?+1,−?3+2?−1}

(ii) {(1,−1,2),(2,0,1),(−1,2,−1)} in ?3 in ?3(?) are linearly dependent or linearly independent

20.Evaluate which of the following sets are bases for ?3 :

(i){(1,0,−1),(2,5,1),(0,−4,3)}(ii){(−1,3,1),(2,−4,−3),(−3,8,2)}

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