MA8352 Important 16 mark Questions Linear Algebra and Partial Differential Equations

MA8352 Important 16 Mark Questions Linear Algebra and Partial Differential Equations Regulation 2017 Anna University free download. Linear Algebra and Partial Differential Equations Important 16 Mark Questions MA8352 pdf free download.

Sample MA8352 Important 16 Mark Questions Linear Algebra and Partial Differential Equations:

1.(a) In any vector space ????, prove that the following statements are true :
i) 0.????=0 for each ????∈????
ii) (−????)????=−(????????) for each ????∈???? and each ????∈????
iii) ????.0=0 for each ????∈????
BTL3Applying

1. (b)Let ???? be the set of all polynomials of degree less than or equal to n with real coefficients. Show that ???? is a vector space over???? with respect to polynomial addition and usual multiplication of real numbers with a polynomial.
BTL3Applying MA8352 Important 16 Mark Questions Linear Algebra and Partial Differential Equations

2. (a)If ????,???? and ???? are vectors in a vector space ???? such that ????+????=????+???? then prove that ????=????
ii) The vector 0 (identity) is unique
iii) The additive identity for any ????∈???? is unique
BTL4Analyzing

2.(b)Point out that the set of all ????×???? matrices with entries from a field F is a vector space denoted as ????????×????(????) with the operations of matrix addition and scalar multiplication is a vector space
BTL4Analyzing MA8352 Important 16 Mark Questions Linear Algebra and Partial Differential Equations

3. (a)Let ???? be a vector space and ???? a subset of????. Prove that???? is a subspace of ???? if and only if the following three conditions hold for the operations defined in????:
i) 0∈????ii) ????+????∈???? whenever ????∈???? and ????∈????
iii) ????????∈???? whenever ????∈???? and ????∈????

3.(b)Evaluate that the set of all real valued continuous (differentiable or integrable) functions of ???? defined in some interval [0,1] is a vector space.
BTL5Evaluating MA8352 Important 16 Mark Questions Linear Algebra and Partial Differential Equations

4. (a)i) Prove that any intersection of subspaces of a vector space ???? is a subspace of ????
ii) Prove that the union of two subspaces is not necessarily a subspace
BTl3Applying

4.(b)Analyse that the set of all convergent sequences is a vector space over the field of real numbers
BTL4 Analyzing MA8352 Important 16 Mark Questions Linear Algebra and Partial Differential Equations

5. (a)Describe that the union of two subspaces ????1 and ????2 is a subspace if and only if one is contained in the other
BTL1 Remembering

5.(b)Illustrate that set of all diagonal matrices of order ????×???? is a subspace of the vector space ????????×????(????), where ????????×???? is the set of all square matrices over the field FBTL2 Understanding MA8352 Important 16 Mark Questions Linear Algebra and Partial Differential Equations

6. (a)Prove that the span of any subset ???? of a vector space ???? is a subspace of ????. Moreover, any subspace of ???? that contains ???? must also contain the span of ????
BTL3Applying

6.(b)Evaluate that ????1={(????1,????2,…????????)∈????????;????1+????2+⋯+????????=0} is a subspace of ???????? and ????2={(????1,????2,…????????)∈????????;????1+????2+⋯+????????=1} is not a subspace
BTL5Evaluating MA8352 Important 16 Mark Questions Linear Algebra and Partial Differential Equations

7. (a)Prove that the span of any subset S of a vector space ???? is the smallest subspace of ???? containing????.

 

Subject name	Linear Algebra and Partial Differential Equations
Semester	3
Subject Code	MA8352
Regulation	2017 regulation

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