**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 𝑥3−2𝑥2+1,4𝑥2−𝑥+3 and 3𝑥−2 generate 𝑃3(𝑅)? Justify your answer.

5.Is {(1,4,−6),(1,5,8),(2,1,1),(0,1,0)} is a linearly independent subset of 𝑅3 ? Justify your answer

6.The vectors 𝑢1=(2,−3,1),𝑢2=(1,4,−2),𝑢3=(−8,12,−4),𝑢4=(1,37,−17) and 𝑢5=(−3,−5,8) generate 𝑅3. Find a subset of the set {𝑢1,𝑢2,𝑢3,𝑢4,𝑢5} that is a basis for 𝑅3

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

8.Write the vectors 𝑣=(1,−2,5) as a linear combination of the vectors 𝑥=(1,1,1),𝑦=(1,2,3) and 𝑧=(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={(𝑎1,𝑎2,𝑎3)𝛜𝑅3:𝑎1+2𝑎2-3𝑎3=1} is a subspace of 𝑅3 under the operations of addition and scalar multiplication

11.Determine whether 𝑤=(4,−7,3) can be written as a linear combination of 𝑣1=(1,2,0) and 𝑣2=(3,1,1) in 𝑅3

12.For which value of k will the vector 𝑢=(1,−2,𝑘) in 𝑅3 be a linear combination of the vectors 𝑣=(3,0,−2) and 𝑤=(2,−1,5)?

13.Determine whether the set 𝑊1={(𝑎1,𝑎2,𝑎3)∈𝑅3∶ 𝑎1=𝑎3+2} is a subspace of 𝑅3 under the operations of addition and scalar multiplication defined on 𝑅3

14.Point out whether the set 𝑊1={(𝑎1,𝑎2,𝑎3)∈𝑅3∶ 𝑎1−4𝑎2−𝑎3=0} is a subspace of 𝑅3 under the operations of addition and scalar multiplication defined on 𝑅3

15.Check whether 2𝑥3−2𝑥2+12𝑥−6 is a linear combination of𝑥3−2𝑥2−5𝑥−3 and 3𝑥3−5𝑥2−4𝑥−9

16.Point out whether 𝑤=(3,4,1) can be written as a linear combination of 𝑣1=(1,−2,1) and 𝑣2=(−2,−1,1) in 𝑅3

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

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

ii) 2𝑥3−𝑥2+𝑥+3,𝑆={𝑥3+𝑥2+𝑥+1,𝑥2+𝑥+1,𝑥+1}

18.Show that the vectors {(1,1,0),(1,0,1) and (0,1,1)} genarate 𝐹3

19.Check whether the vectors (i) {𝑥3+2𝑥2,−𝑥2+3𝑥+1,−𝑥3+2𝑥−1}

(ii) {(1,−1,2),(2,0,1),(−1,2,−1)} in 𝑅3 in 𝑃3(𝑅) are linearly dependent or linearly independent

20.Evaluate which of the following sets are bases for 𝑅3 :

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

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