{\text{Let A be the matrix of order 2}} \times {\text{3 and B be the matrix of order 3}} \times {\text{5,then which of the following is the order of the matrix AB?}}

• A) 2 \times 3
• B) 3 \times 3
• C) 2 \times 5
• D) 3 \times 5

An m x m ______ matrix is only square matrix that is both unit lower triangular and upper triangular.

• A) Scalar
• B) Diagonal
• C) Null
• D) Identity

Which of the following is the most suitable option while doing LU-factorization?

• A) Entries cannot be interchanged.
• B) Columns can be interchanged.
• C) Rows can be interchanged.
• D) Rows cannot be interchanged.

The matrix $ M = \left[ {\,\begin{array}{*{20}{c}} a&4&5&6\\\7&a&4&5\\\8&7&a&4\\\9&8&7&a \end{array}\,} \right]$ is a ______ matrix.

• A) Toeplitz
• B) Rectangular
• C) Diagonal
• D) Identity

If M=[3] then which of the following is the determinant of the matrix M?

• A) [3]
• B) 1
• C) 3
• D) [1]

If |D|=ad-bc is a determinant of an n x n matrix D then at what condition matrix D is invertible?

• A) When |D|=ad-bc=0
• B) When |D|=ad-bc is not equal to zero
• C) When |D|=ad-bc=|2|
• D) When |D|=ad-bc= [0 2]

If a multiple of one row of a square matrix A is added to another row to produce a matrix B, then which of the following condition is true?

• A) det(B). det(A) = det(A)
• B) det(A). det(B) = 0
• C) det(B) = k det(A)
• D) det(B) = det(A)

If a matrix A is invertible than adj(A) is also invertible.

• A) FALSE
• B) TRUE
• C)
• D)

If the absolute value of each diagonal entry exceeds the sum of the absolute values of the other entries in the same row then a matrix A is called:

• A) diagonally
• B) scalar
• C) invertible
• D) strictly diagonally dominant

According to determinant properties, the determinants of resulting matrix equal to k delta if elements of rows are-------

• A) Subtracting to constant k
• B) Multiplied to constant k
• C) Divided to constant k
• D) Added to constant k

At what condition the Cramer’s formula is valid for linear systems?

• A) When det(A) is equal to zero
• B) When matrix is m x n
• C) When matrix is n x n
• D) When det(A) in not equal to zero

If all the elements of one row is ‘0’ in a matrix A then which of the following about the determinant of the matrix is true?

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

Why inverse of the matrix A= [1 2] is NOT possible?

• A) Because it is an identity matrix.
• B) Because it is a square matrix.
• C) Because it is a rectangular matrix
• D) Because it is a zero matrix.

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