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

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

• A) 15
• B) 7
• C) 8
• D) 0

A determinant does not change if we add a multiple of a row to another row.

• A) False
• B) True
• C)
• D)

Which of the following is the area of the parallelogram determined by the columns of A where A is a 2 x 2 matrix?

• A) A^(-1) ,that is inverse of A
• B) det A
• C) [A]
• D) |det A|

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

• A) 7
• B) 15
• C) 0
• D) 8

Which of the following is the volume of the parallelepiped determined by the columns of A where A is

• A) det A
• B) |det A|
• C) A^(-1) ,that is inverse of A
• D) [A]

If A is a square matrix, then the Minor of entry ith row and jth column is to be the determinant of the sub matrix that remains when the ith row and jth column of A are:

• A) Multiplied
• B) Added
• C) Divided
• D) Deleted

In general,

• A) det(A+B)≠ detA+detB
• B) det(A+B)=det(A)+det(B)
• C)
• D)