LU-factorization is used to solve systems of linear equations or calculate the ______.

• A) Column
• B) Determinant
• C) Diagonal
• D) Row

If two rows of a square matrix A are interchanged to produce B, then

• A) none of the above
• B) debt=-detA
• C) detB=detA
• D) detB=detA

If all the entries of a row or a column of a square matrix are zero, then det (A) will be _____________.

• A) Infinity
• B) Non zero
• C) One
• D) Zero

If A is not invertible matrix, then

• A) Det(A)=1
• B) Det(A)=0
• C) \det \left( A \right) \ne 0
• D) Det(A)=-1

If A is an n×n matrix, then

• A) \det {A^T} = -detA
• B) \det {A^T} = detA
• C)
• D)

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

• A) It has at least one zero along its main diagonal.
• B) It has no zeros along its main diagonal.
• C) It has more than two zeros along its main diagonal.
• D) It has two zeros along its main diagonal.

If the coefficient matrix is large and with a high proportion of zero entries, then which of the following works quickly in favor of solving a linear systems for saving less computer memory?

• A) Row-echelon method
• B) Direct method
• C) Reduced row-echelon method
• D) Iterative method

The determinant of a square matrix A = \left[ {\begin{array}{*{20}{c}} 3&2\\4&5 \end{array}} \right] is

• A) 7
• B) 0
• C) 8
• D) 15

At what condition the Cramer’s rule fails?

• A) The coefficient matrix A is not invertible.
• B) When the determinant of the coefficient matrix is not zero.
• C) When the determinant of the coefficient matrix is zero.
• D) When matrix is n x n.

If M is a square matrix having two rows equal then which of the following about the determinant of the matrix is true?

• A) det(M)=1
• B) det(M) is not equal to '0'
• C) det(M) is not equal to '1'
• D) det(M)=0

If A is an n \times n matrix, then

• A) \det {A^T} = detA
• B) \det {A^T} = -detA
• C)
• D)

If A and B are n\times n matrices, then

• A) det(AB)=detA.detB
• B) none of the above.
• C) det(AB)=detA+detB
• D) det(AB)=detA-detB

If det(A) = 187 then the Cramer’s rule can be applicable because:

• A) The coefficient matrix A is scalar.
• B) The coefficient matrix A is invertible.
• C) The coefficient matrix A is m x n.
• D) The coefficient matrix A is not invertible.

For any 3x3 matrix A where det (A) = 3, then det (2A) = ________.

• A) 24
• B) 20
• C) 15
• D) 6

At what condition det(AB)=(detA)(detB) is possible?

• A) When A is a row matrix
• B) When A and B are m x n matrices
• C) When A and B are n x n matrices
• D) When B is a column matrix

The determinant of the identity matrix is ______

• A) 0
• B) -1
• C) 1
• D) n x (number of rows or coulms)

Any matrix A and its transpose have the same determinant.

• A) True
• B) False
• C)
• D)

Jacobi’s method assumes that the diagonal entries of an invertible matrix A are all

• A) non-zero
• B) zero
• C)
• D)

If A is a triangular matrix, then det(A) is the product of the entries on the ________.

• A) First two rows of A
• B) Main diagonal of A
• C) Diagonal of A
• D) First two columns of A

If both the Jacobi and Gauss-Seidel sequences converge for the solution of Ax=b, for any initial x(0), then which of the following is true about both the solutions?

• A) Different solutions
• B) Unique solution
• C) No solution
• D) Infinitely many solutions