vu mth501 Final Term - Quiz No.1
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: Which of the following will be the Linear Combination corresponding to \(\begin{pmatrix} -2 & 3 \ 5 & 1 \ end{pmatrix}\begin{pmatrix} x \ y \ end{pmatrix} \)?
\( \begin{pmatrix} -2 \ 3 \ end{pmatrix} x + \begin{pmatrix} 5 \ 1 \ end{pmatrix} y \)
\( \begin{pmatrix} 3 \ 1 \ end{pmatrix} x + \begin{pmatrix} -2 \ 5 \ end{pmatrix} y \)
\( \begin{pmatrix} 5 \ 1 \ end{pmatrix} x + \begin{pmatrix} -2 \ 3 \ end{pmatrix} y \)
\( \begin{pmatrix} -2 \ 5 \ end{pmatrix} x + \begin{pmatrix} 3 \ 1 \ end{pmatrix} y \)
Question 2: Gauss-Seidel method is also termed as a method of
Elimination Method
False Position Method
Successive Displacement
Iteration Method
Question 3: If \(v_1^r, v_2^r \) and \(v_3^r \) are in \(R^m \) then which of the following is equivalent to \(\begin{bmatrix} v_1 & v_2 & v_3 \ end{bmatrix}\begin{bmatrix} 2 \ -7 \ 5 \ end{bmatrix} \)
\( 2v_1^r - 7v_2^r + 5v_3^r \)
\( 5v_1^r - 7v_2^r + 2v_3^r \)
\( 5v_1^r + 2v_2^r - 7v_3^r \)
\( 2v_1^r + 5v_2^r - 7v_3^r \)
Question 4: If \( v_1^r = (2, 1), v_2^r = (3, 4) \) and \( v_3^r = (7, 8) \) then which of the following is true?
$$ {v_1^r, v_2^r, v_3^r} $$ is linearly dependent.
$$ {v_1^r, v_2^r, v_3^r} $$ is linearly independent.
The vector equation has trivial solution.
\( v_1^r = {2 over 3} v_2^r \)
Question 6: If T be a transformation, then which of the following is true for its linearity?
$$ T(cu^r , gdv^r) = cT(u^r) gd T(v^r) ; ;;;; $$ whre 'c' and 'd' are scalars
$$ T(cu^r + dv^r) = cT(u^r) + dT(v^r); ;;;; $$ whre 'c' and 'd' are scalars
$$ T(cu^r × dv^r) = cT(u^r) × dT(v^r); ;;;; $$ whre 'c' and 'd' are scalars
$$ T(cu^r + dv^r) = dT(u^r) + cT(v^r); ;;;; $$ whre 'c' and 'd' are scalars
Question 7: Which of the following is the coefficient matrix for the system \(\begin{matrix} x_1 - 2x_2 + x_3 = 0 \ 2x_2 - 7x_3 = 8 \ -4x_1 + 3x_2 + 9x_3 = -6 end{matrix} \)
\( \begin{bmatrix} 1 & -2 & 1 \ 0 & 2 & -7 \ -4 & 3 & 9 \ end{bmatrix} \)
\( \begin{bmatrix} 1 & -2 & 0 \ 0 & 2 & 8 \ -4 & 3 & -6 \ end{bmatrix} \)
\( \begin{bmatrix} 1 & 1 & 0 \ 0 & -7 & 8 \ -4 & 9 & -6 \ end{bmatrix} \)
\( \begin{bmatrix} 1 & 0 & -4 \ -2 & 2 & 3 \ 1 & -7 & 9 \ end{bmatrix} \)
Question 8: Two simultaneous linear equations in two variables have no solution if their corresponding lines are __________.
parallel and distinct
intersecting
coincident
perpendicular
Question 9: Which of the following is true for the matrix \(\begin{bmatrix} 1 & 0 & 0 \ 0 & 2 & 0 \ 0 & 0 & 3\ end{bmatrix} \)?
It is a null matrix.
It is a scalar matrix.
It is a diagonal matrix.
It is an identity matrix.
