MTH501 Solved MCQs

MTH501- Linear Algebra MCQS MIDTERM EXAMINATION ~“LIBRIANSMINE”~

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
2. Onto

Correct answer: One-to-one

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

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
2. det kA = det (k+A)
3. det k A = k2 det A
4. det A = k.det A

Correct answer: det k A = k2 det A

Q4. The equation x = p + t v describes a line (1 marks)

1. through v parallel to p
2. through p parallel to v
3. through origin parallel to p

Correct answer: through p parallel to v

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

v v

v v

v v

(lec 8 ) hint* vector v1 is a multiple of v2

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

1. True
2. False

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

1. True
2. False

Correct answer: True

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

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

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

1. True
2. False

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

i j