MTH501 Midterm Past Paper 6

Q1. If A is a 2 2 (1 marks)

 matrix, the area of the parallelogram determined by the columns of A is

A

1. det A
2. adj A

Q2. Cramer’s rule leads easily to a general formula for (1 marks)

1. the inverse of an n n

 matrix A

1. the adjugate of an n n

 matrix A

1. the determinant of an n n

 matrix A

Q3. The transpose of an upper triangular matrix is (1 marks)

1. lower triangular matrix
2. upper triangular matrix
3. diagonal matrix

Q4. Let A be a square matrix of order 3 3 (1 marks)

 with det( ) A  , then det(2 ) A 

1. 168
2. 186
3. 21
4. 126

Q5. A basis is a linearly independent set that is as large as possible. (1 marks)

1. True
2. False

Q6. Col (1 marks)

A is all of m if and only if

1. the equation

Ax  has a solution for each b in m

1. the equation Ax

b has a solution for each b in m

1. the equation Ax

b has a solution for a fixed b in m

Q7. If A (1 marks)

A A A A

and B B B

, then the partitions of A and B

1. are not conformable for block multiplication
2. are conformable for AB block multiplication
3. are not conformable for BA block multiplication

Q8. Two vectors are linearly dependent if and only if they lie (1 marks)

1. on a line parallel to x-axis
2. on a line through origin
3. on a line parallel to y-axis

Q9. 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

Q10. Let A be an m n (1 marks)

matrix. If for each b in m the equation Ax=b has a solution then

1. A has pivot position in only one row
2. Columns of A span

m

1. Rows of A span

m

Q11. Given the system (1 marks)

x x x x x x x x

the augmented matrix for the system is