MTH501 Midterm Objective

MTH501

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

1. one-to-one
2. onto

Correct answer: one-to-one

Q2. Which one of the following is an matrix?

Q3. Let

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 kA = det A

Correct answer: det kA= k det A

The equation x = p + t v describes a line

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.

v v

v v

v v

Q6. Every linear transformation is a matrix transformation

1. True
2. False

Correct answer: True

Q7. A null space is a vector space.

1. True
2. False

Correct answer: True

Q8. If two row interchanges are made in succession, then the new determinant

1. equals to the old determinant
2. equals to -1 times the old determinant

Correct answer: equals to 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. 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

Correct answer: the number of row interchanges made during row reduction from A to U

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

1. True