Q2. 03 Find the rank of the matrix04

This is question 2 (null marks) from the GTU Vector Calculus and Linear Algebra BE Winter 2021 question paper. Subject code: 2110015.

Q2. Find the inverse of matrix using Row operation.

This is question 2 (7 marks) from the GTU Vector Calculus and Linear Algebra BE Winter 2021 question paper. Subject code: 2110015.

Q3. Does is a subspace of with standard operation?

This is question 3 (3 marks) from the GTU Vector Calculus and Linear Algebra BE Winter 2021 question paper. Subject code: 2110015.

Vector Calculus And Linear Algebra | B.E. Semester 1 Winter 2021 | GTU Papers

Q: Q1. Objective Question (MCQ) 1. Let Abe a unitary matrix then is (A) A (B) ( C ) (D) 2. For which value of k, u = (2,1,3) and v = (1,7,k) are orthogonal? (A) k =1 (B) k=3 ( C ) k =2 (D)None of these 3. The dimension of the solution space of is (A) 1 (B) 2 ( C) 3 (D) 4. The mapping defined by is called as (A) Reflection (B) Magnification ( C) Rotation (D) Projection 5. Let be linear operator defined by , what is basis for (D) None of these (A) (B) ( C) 6. What is angle between two vectors u= (1,0,1,0) and v = (-3,-3,-3,-3)? (A) (B) ( C) (D) 7. The column vectors of an orthogonal matrix are (A) Orthogonal (B)Orthonormal (C) Dependent (D)None of these

This is question 1 (4 marks) from the GTU Vector Calculus and Linear Algebra BE Winter 2021 question paper. Subject code: 2110015.

Q: Q1. Objective Question (MCQ) 1. What is an eigenvalue of ? (A) 8 (B) 2 ( C) 3 (D) 1 2. Cayley Hamilton theorem holds for _______ matrices only. (A) Singular (B) All square ( C) Null (D)Afew rectangular 3. If then _____. (A) r (B) ( C) (D) None of these 4. is _______? (A) Solenoidal (B) Irrotational ( C) Both (D) None of these 5. The matrix of a quadratic form is a _________ matrix. (A) Symmetric (B)Skew symmetric ( C) Hermitian (D) Skew hermitian 6. The value of the line integral from (0,1,-1) to (1,2,0) is____. (A)-1 (B) 3 ( C) 0 (D) None of these 7. The value of line integral does not depend on path Cthen is (A) Solenoidal (B)Incompressible (C) Irrotational (D) None of these

This is question 1 (7 marks) from the GTU Vector Calculus and Linear Algebra BE Winter 2021 question paper. Subject code: 2110015.

Q: Q3. Check whether the set is linearly independent or linearly dependent in

This is question 3 (4 marks) from the GTU Vector Calculus and Linear Algebra BE Winter 2021 question paper. Subject code: 2110015.

Q: Q3. Determine the dimension and a basis for the solution space of the system of equation:

This is question 3 (7 marks) from the GTU Vector Calculus and Linear Algebra BE Winter 2021 question paper. Subject code: 2110015.

Q: Q4. Show that the transformation defined by is linear.

This is question 4 (3 marks) from the GTU Vector Calculus and Linear Algebra BE Winter 2021 question paper. Subject code: 2110015.

Q: Q4. Consider the basis , be the linear transformation such that . Find

This is question 4 (4 marks) from the GTU Vector Calculus and Linear Algebra BE Winter 2021 question paper. Subject code: 2110015.

Questions20

Objective Question (MCQ) 1. Let Abe a unitary matrix then is (A) A (B) ( C ) (D) 2. For which value of k, u = (2,1,3) and v = (1,7,k) are orthogonal? (A) k =1 (B) k=3 ( C ) k =2 (D)None of these 3. The dimension of the solution space of is (A) 1 (B) 2 ( C) 3 (D) 4. The mapping defined by is called as (A) Reflection (B) Magnification ( C) Rotation (D) Projection 5. Let be linear operator defined by , what is basis for (D) None of these (A) (B) ( C) 6. What is angle between two vectors u= (1,0,1,0) and v = (-3,-3,-3,-3)? (A) (B) ( C) (D) 7. The column vectors of an orthogonal matrix are (A) Orthogonal (B)Orthonormal (C) Dependent (D)None of these

[4 marks]

Objective Question (MCQ) 1. What is an eigenvalue of ? (A) 8 (B) 2 ( C) 3 (D) 1 2. Cayley Hamilton theorem holds for _______ matrices only. (A) Singular (B) All square ( C) Null (D)Afew rectangular 3. If then _____. (A) r (B) ( C) (D) None of these 4. is _______? (A) Solenoidal (B) Irrotational ( C) Both (D) None of these 5. The matrix of a quadratic form is a _________ matrix. (A) Symmetric (B)Skew symmetric ( C) Hermitian (D) Skew hermitian 6. The value of the line integral from (0,1,-1) to (1,2,0) is____. (A)-1 (B) 3 ( C) 0 (D) None of these 7. The value of line integral does not depend on path Cthen is (A) Solenoidal (B)Incompressible (C) Irrotational (D) None of these

[7 marks]

03 Find the rank of the matrix04

[ marks]

Find the inverse of matrix using Row operation.

[7 marks]

Determine whether the set of all positive real number with and is a vector space.

[ marks]

Does is a subspace of with standard operation?

[3 marks]

Check whether the set is linearly independent or linearly dependent in

[4 marks]

Determine the dimension and a basis for the solution space of the system of equation:

[7 marks]

Show that the transformation defined by is linear.

[3 marks]

Consider the basis , be the linear transformation such that . Find

[4 marks]

Let have inner product Use the Gram Schmidt process to transform the basis vectors into an orthonormal basis.

[7 marks]

Determine algebraic and geometric multiplicity of each eigen value of

[3 marks]

04 Find the inverse of the matrix using Caley –Hamilton theorem. Find the matrix Psuch that diagonalizes the matrix and hence

[ marks]

07 determine

[ marks]

Find the gradient of at (1,1,1).

[3 marks]

Prove that , is irrotational and find its scalar potential.

[4 marks]

Find the least square solution of the linear system , given by , and find the orthogonal projection of b on the column space of A.

[7 marks]

Find the work done by03

[ marks]

04 Evaluate along the parabola between the points Verify Green’s theorem for the function and Cis the

[ marks]

07 path rectangle in the xy plane bounded by

[ marks]

Vector Calculus and Linear Algebra — Winter 2021

Questions20

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