MTH501 Quiz 1 Lectures 8-15 by Junaid

Q1. If a matrix equation is solved using the Jacobi’s method. Then which of the following is true about its main diagonal?

1. It has two zeros along its main diagonal.
2. It has at least one zero along its main diagonal
3. It has more than one zero along its main diagonal
4. It has no zero along its diagonal.

Q2. As soon as an approximate solution of a linear system is sufficiently accurate for practical work than which of the following is true for an iterative process?

1. The process may be stopped.
2. The reduced row-echelon method may be used.
3. The row-echelon method may be used.
4. The process may be stopped.

Q3. If determinant of a matrix is not zero then which of the following is true for that system?

1. The inversion method is applies.
2. The inversion method is fails.

Q4. A partitioned matrix “A” is said to be block diagonal if the matrices on the main diagonal are square and all other position matrices are

1. Non zero skew symmetric
2. Nonzero symmetric
3. Unit
4. Zero

Q5. If A is strictly diagonal dominant matrix. Then which of the following is true for A.

1. It is a singular matrix.
2. It is a rectangular matrix.
3. It is an invertible matrix.
4. It is a null matrix.

Q6. A matrix can be subdivided into sub matrices in various ways by inserting lines between selected _________ and columns.

1. Elements
2. Rows
3. Blocks
4. Diagonals.

Q7. The determinant of a triangular matrix is the sum of the entries of the main diagonal

1. True
2. False

Q8. What is the maximum possible number of pivots in a ‘3by 3’ matrix?

1. 0
2. 3
3. 1
4. 5

Q9. Let A be a square n×n matrix. Then which of the following statement(s) is(are) equivalent?

1. A row is equivalent to the n×n identity matrix.
2. A has n pivot positions.
3. Options (b to d).
4. A is an invertible matrix.

Q10. What is the maximum possible number of pivots in a 4×6 matrix?

1. 4
2. 8
3. 6
4. 10

Q11. In LU-decomposition, if A is the square matrix of order m, then the order of both lower and upper triangular matrices will be __________.

1. 𝑚+ 1
2. 2
3. m

Q12. A sufficient condition for the Jacobi’s method to converge for the linear system Ax=b

1. A is diagonally dominant
2. A is non singular
3. None of the above
4. A-I is diagonally dominant

Q13. An m×m ________matrix is only square matrix that is both unit lower triangular and upper triangular.

1. Scalar
2. Null
3. Identity
4. Diagonal

Q14. A homogeneous linear system always has the trivial solution; there are only two possibilities for its solutions:

1. None of the given.
2. Both c and
3. The system has only the trivial solution.
4. The system has infinitely many solutions in addition to the trivial solution.

Q15. A null space is the vector space.

1. False
2. True

Q16. LU-factorization is used to solve system of linear equations are calculate the_______.

1. Row
2. Column
3. Diagonal
4. Determinant

Q17. Let A be the matrix of order 2×3 and B be the matrix of order 3×5, then which of the following is the order of the matrix AB?

1. 2×3
2. 3×5
3. 3×3
4. 2×5
5. LU-decomposition converts the problem of solving the single system A x=b into the problem of solving the two systems. Ly=b and U x=y. these systems are easy to solve because their co-efficient matrices are________.