Download OU B.Sc Computer Science 5th Sem Linear Algebra Important Questions

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Linear Algebra

Unit-1

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1. Definition of:
   1. Vector Space
   2. Subspace
   3. Linear Span
   4. Linear Combination
   5. Linear Integral

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   6. Linear Dependence
   7. Null Space
   8. Column Space
   9. Linear Transformation

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2. Theorems on necessary and sufficient condition of subspace and problems.
3. Algebra of subspace
4. If S is subset of vector space V(F) then P.T.
   1. S is Subspace of V =>L(S)=S
   2. L(L(s))=L(s)

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5. If S, T are subset of Vector space V(F) then
   1. SCT =>L(S)CL(T)
   2. L(SUT) = L(S)+L(T)
6. Basis Extension theorem and problems.
7. Problems on Linear Transformation.

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8. Let u,v be two Vector Spaces and T:u-V is L>T then range set R(T) and Null space N(T) is a Subspace of U(F)
9. Rank Nullity theorem and dimensions theorems.

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1. All theorems in Rank

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2. Problems in Change of basis, Eigen value and Eigen vector and Characteristic equation.

Unit-3

1. Theorems and problems in Diagonalization.
2. An nXn matrix with n-distinct eigen values is diagonalizable.
3. Problems in Complex Eigen value and application of Differential equation problems.

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4. Definition of:
   1. Orthogonal vector
   2. Orthonormal vector
   3. Inner product space
   4. Length of a vector
   5. Unit vector

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5. Problems in Inner product space and Orthogonality.
6. All Inequality theorems.
7. Practical problems.

S = {u,, u,, ..., u,} is an orthogonal set of non-zero vectors in R" then S is linear independent and hence, is a basis for the subspace spanned by S.

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