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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