**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 ?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.

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MA8352 LAPDE Important Questions

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