vu mth501 Final Term - Quiz No.2
vu mth501 Linear Algebra Quiz
This quiz belongs to book/course code vu mth501 Linear Algebra of vu organization. We have 4 quizzes available related to the book/course Linear Algebra. This quiz has a total of 10 multiple choice questions (MCQs) to prepare and belongs to topic Final Term. NVAEducation wants its users to help them learn in an easy way. For that purpose, you are free to prepare online MCQs and quizzes.
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Question 1: If the determinant of the matrix \( A =\begin{bmatrix} 2 & 3 & 4 \ 1 & 2 & 2 \ 3 & 4 & 5 \ end{bmatrix} \) is -1 and the matrix B is obtained by adding 2 times of the second row in the first row of the matrix A, then which of the following is true for the matrix B?
Its determinant is -1.
Its determinant is 1.
Its determinant can not be evaluated.
The information is not sufficient to calculate the determinant.
Question 2: If \( Ax^r = b^r \) and factorization of A is LU, then which of the following pair of equations can be used to solve \( LUx^r = b^r \) for value of &\( x^r \)?
\( Ux^r = y^r $$ and $$ Ly^r = b^r \)
\( Lx^r = y^r $$ and $$ Uy^r = b^r \)
\( Ub^r = y^r $$ and $$ Ly^r = x^r \)
\( Lb^r = y^r $$ and $$ Uy^r = x^r \)
Question 3: 7x is an algebraic term in which 7 is a __________ and x is a __________.
term, expression
coefficient, variable
variable, coefficient
numerical, alphabet
Question 5: The equation: \(\begin{pmatrix} -2 & 3 \ 5 & 1 \ end{pmatrix}\begin{pmatrix} x \ y \ end{pmatrix} =\begin{pmatrix} -7 \ 4 \ end{pmatrix} \) will have the solution only if __________.
\( \begin{pmatrix} -7 \ 4 \ end{pmatrix} = x \begin{pmatrix} 3 \ 1 \ end{pmatrix} + y \begin{pmatrix} -2 \ 5 \ end{pmatrix} \)
\( \begin{pmatrix} -7 \ 4 \ end{pmatrix} = x \begin{pmatrix} -2 \ 5 \ end{pmatrix} + y \begin{pmatrix} 3 \ 1 \ end{pmatrix} \)
\( \begin{pmatrix} -7 \ 4 \ end{pmatrix} = x \begin{pmatrix} -2 \ 3 \ end{pmatrix} + y \begin{pmatrix} 5 \ 1 \ end{pmatrix} \)
\( \begin{pmatrix} -7 \ 4 \ end{pmatrix} = x \begin{pmatrix} 5 \ 1 \ end{pmatrix} + y \begin{pmatrix} -2 \ 3 \ end{pmatrix} \)
Question 6: What is Eigen value?
A vector obtained from the coordinates
A matrix determined from the algebraic equations
A scalar associated with a given linear transformation
Question 7: Since every linear transformation $$T : R^n \rightarrow R^m \( is actually matrix transformation, then which of the following is the alternate notation for the transformation?
\( Ax^r ; a ;; x^r \)
\( Ax^r ; a ;; T(x^r) \)
\( x^r ; a ;; Ax^r \)
\( T(x^r) ; a ;; Ax^r \)
Question 10: Why inverse of the matrix A= [1 2] is NOT possible?
Because it is a saquare matrix.
Because it is a zero matrix.
Because it is an identity matrix,
Because it is rectahular matrix.
