vu mth501 Final Term - Quiz No.3
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: A homogeneous linear system always has the trivial solution: there are only two possibilities for its solutions:
The system has only the trivial solution
The system has infinitely many solutionsnin addition to trivial solution
Both (a) and (b)
None of the above
Question 2: If \( A =\begin{bmatrix} 0 & 1 & 0 \ 1 & 0 & 0 \ 0 & 0 & 1 \ end{bmatrix} \), then which of the following is true for A?
det(A) = 1
det(A) = - 1
det(A) = 0
det(A) = ±1
Question 3: \(9x^2 + 3x + 4 \) is __________.
an equation
a term
an algebraic expression
quadratic equation
Question 4: If \( X =\begin{bmatrix} M \ N \ end{bmatrix} \) and \( Y=\begin{bmatrix} Q & P \ end{bmatrix} \) whare \(mathbf{M, N, Q}\) and \(mathbf{P}\) are saqure sub-matrices of same size), then Which of the following is possible?
The product $$mathbf{XY}$$ and $$mathbf{YX}$$ both are not defined
The product $$mathbf{XY}$$ and $$mathbf{YX}$$ both are defined
The product $$mathbf{XY}$$ is defied but $$mathbf{YX}$$ is not defined
None of the given
Question 5: The solution of Ax = b exists if and only if b can be written as a linear combination of __________ of A.
columns
rows
both columns and rows
elements
Question 6: If one of the eigenvalues of \(\begin{bmatrix} A end{bmatrix} _{n×n} \) is zero, it implies __________
The solution to $$ egin{bmatrix} A end{bmatrix} egin{bmatrix} X end{bmatrix} = egin{bmatrix} C end{bmatrix}$$ a system of equations is unique
The determinant of $$ egin{bmatrix} A end{bmatrix} $$ is zero
The solution to $$ egin{bmatrix} A end{bmatrix} egin{bmatrix} X end{bmatrix} = egin{bmatrix} 0 end{bmatrix}$$ system of equations is trivial
The determinant of $$ egin{bmatrix} A end{bmatrix} $$ is nonzero
Question 8: Which of the following will be the Matrix Product corresponding to Linear Combination: \(\begin{pmatrix} -2 \ 5 \ end{pmatrix} x +\begin{pmatrix} 3 \ 1 \ end{pmatrix} y \)?
\( \begin{pmatrix} 1 & -3 \ -5 & -2 \ end{pmatrix} \begin{pmatrix} x \ y \ end{pmatrix} \)
\( \begin{pmatrix} -2 & 5 \ 3 & 1 \ end{pmatrix} \begin{pmatrix} x \ y \ end{pmatrix} \)
\( \begin{pmatrix} -2 & 3 \ 5 & 1 \ end{pmatrix} \begin{pmatrix} x \ y \ end{pmatrix} \)
\( \begin{pmatrix} 3 & -2 \ 1 & 5 \ end{pmatrix} \begin{pmatrix} x \ y \ end{pmatrix} \)
Question 9: If the equation: \(\begin{pmatrix} -2 & 3 \ 5 & 1 \ end{pmatrix}\begin{pmatrix} x \ y \ end{pmatrix} =\begin{pmatrix} b_1 \ b_2 \ end{pmatrix} \) has the solution for all \(b_1, b_2 in R \), then \(\begin{pmatrix} b_1 \ b_2 \ end{pmatrix} in \) __________.
Span$$ egin{Bmatrix} egin{pmatrix} -2 \ 3 \ end{pmatrix} , egin{pmatrix} 5 \ 1 \ end{pmatrix} end{Bmatrix} $$
Span$$ egin{Bmatrix} egin{pmatrix} -2 \ 1 \ end{pmatrix} , egin{pmatrix} 5 \ 3 \ end{pmatrix} end{Bmatrix} $$
Span$$ egin{Bmatrix} egin{pmatrix} 3 \ -2 \ end{pmatrix} , egin{pmatrix} 1 \ 5 \ end{pmatrix} end{Bmatrix} $$
Span$$ egin{Bmatrix} egin{pmatrix} -2 \ 5 \ end{pmatrix} , egin{pmatrix} 3 \ 1 \ end{pmatrix} end{Bmatrix} $$
Question 10: Which of the following is the simplified form of \(-1\begin{bmatrix} -1 & 2 \ end{bmatrix} +\begin{bmatrix} 2 & 3 \ end{bmatrix} \)
\( \begin{bmatrix} 3 & -1 \ end{bmatrix} \)
\( \begin{bmatrix} -3 & 1 \ end{bmatrix} \)
\( \begin{bmatrix} 3 & 1 \ end{bmatrix} \)
\( \begin{bmatrix} -3 & -1 \ end{bmatrix} \)
