**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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MA8352 Answer Key, LAPDE Unit wise Important Questions- ECE 3rd Semester