MA8352 LAPDE Important Questions, LINEAR ALGEBRA AND PARTIAL DIFFERENTIAL EQUATIONS –ECE 3rd Sem

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MA8352 LAPDE Important Questions

Anna University Regulation 2017 ECE MA8352 LAPDE Important Questions with Answer Key and ECE 3rd Sem MA8352 LINEAR ALGEBRA AND PARTIAL DIFFERENTIAL EQUATIONS Engineering Answer Key is listed down for students to make perfect utilization and score maximum marks with our study materials.

MA 8352 -LINEAR ALGEBRA AND PARTIAL DIFFERENTIAL EQUATIONS

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 𝑉and 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.

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