Lecture - Linear Algebra I MT22, III
Flashcards
What does it mean if Gauss elimination on $A \in \mathbb{R}^{n\times n}$ gives an upper trianglar matrix with a non-zero diagonal?
$A^{-1}$ exists.
What does it mean if $Ax = 0$ only has one solution, $x = 0$ (for matrices)?
$A$ is invertible.
What does it mean if Gauss-Jordan elimination on $[A \vert I]$ yeilds $[I \vert B]$?
$A^{-1} = B$
What would be the $3 \times 3$ matrix for the ERO corresponding to swapping rows 2 and 3?
What would be the $3 \times 3$ matrix for the ERO corresponding to multiplying row 3 by a constant $\lambda$?
What would be the $3 \times 3$ matrix for the ERO corresponding to adding $\lambda$ lots of row 1 onto row 2?
What is true about the product of two invertible matrices $AB$?
It is also invertible.
What happens to the element $a _ {ij}$ of a matrix when it is transposed?
It becomes $a _ {ji}$.
What is $(A + B)^\top$?
What is $(A^\top)^{-1}$?
What does it mean for a matrix to be symmetric?
What does it mean for a matrix to be skew-symmetric?
What is true about the diagonal entries of a skew-symmetric matrix?
They are zero.