Practice 10 questions on MAT1341 - Linear Algebra at uOttawa - University of Ottawa. Free AI-generated quiz on uNotes — track your score, retake anytime.
1Which of the following conditions correctly describes a set $S$ that is a subspace of $\mathbb{R}^n$?
2Given an $n \times n$ matrix $A$, which of the following statements are equivalent to the assertion that $A$ is invertible?
3What is the result of the Rank-Nullity Theorem for an $m \times n$ matrix $A$?
4If $A$ and $B$ are $n \times n$ matrices, which of the following properties of the determinant is true?
5A linear system $Ax = b$ with $n$ variables has a unique solution if:
6Let $A$ be a $3 \times 3$ matrix with eigenvalue $\lambda = 2$ having algebraic multiplicity 3. Which of the following conditions is necessary for $A$ to be diagonalizable?
7If $A$ is an invertible matrix, what is the correct expression for $(ABA^{-1})^{-1}$?
8Which of the following sets are linearly independent in $\mathbb{R}^2$?
9For a stochastic matrix $M$, a steady-state vector $x$ satisfies which equation?
10If $u$ and $v$ are eigenvectors of $A$ corresponding to distinct eigenvalues $\lambda_1$ and $\lambda_2$, then $u$ and $v$ must be:
