MTH501 Midterm Past Paper 2010

MIDTERM EXAMINATION · Spring 2010 · MTH501- Linear Algebra (Session - 4) Solved by well wisher

Q1. If for a linear transformation the equation T(x)=0 has only the trivial solution then T is (1 marks)

1. one-to-one Page no : 113
2. onto

Correct answer: one-to-one Page no : 113

Q2. Which one of the following is an elementary matrix? (1 marks)

 can be converted into by R2+(-R1)=>R2

Ref: An elementary matrix is a matrix that results from applying a single

elementary row operation to an identity matrix.

Q3. Let (1 marks)

a b A c d

and let k be a scalar .A formula that relates det kA to k and det A is

1. det kA= k det A Page no : 100
2. det kA = det (k+A)
3. det k A = k2 det A
4. det kA = det A

Q4. (1 marks)

1. Through v parallel to p
2. Through p parallel to v Page no : 55
3. Through origin parallel to p

Q5. Determine which of the following sets of vectors are linearly dependent. (1 marks)

v v

v v

 Page no: 85

v v

Q6. Every linear transformation is a matrix transformation (1 marks)

1. True
2. False Page no : 100

Ref: Every matrix transformation is a linear transformation.

Q7. A null space is a vector space. (1 marks)

1. True page no: 270
2. False

Correct answer: True page no: 270

Q8. If two row interchanges are made in succession, then the new determinant (1 marks)

1. equals to the old determinant
2. equals to -1 times the old determinant Page no : 386

Correct answer: equals to -1 times the old determinant Page no : 386

Ref: A row interchange changes the sign of the determinant

Q9. The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)r , Where r is (1 marks)

1. the number of rows of A
2. The number of row interchanges made during row reduction from A to U
3. The number of rows of U
4. The number of row interchanges made during row reduction U to A

Ref:

Q10. If A is invertible, then det(A)=det(A-1)=1. (1 marks)

1. True
2. False

Correct answer: True

Q11. A square matrix (1 marks)

i j A a is lower triangular if and only if i j a for

i j

i j