Find all four \(2 \times 2\) diagonal matrices \(A\) that have the property \(A^{2}=I\). Geometrically interpret each of these examples as linear maps.
Find all four \(2 \times 2\) diagonal matrices...
Find an example of \(2 \times 2\) matrices \(A\) and \(B\) so that \(A B=0\) but \(B A \neq 0\).
Identify which of the following collections of matrices form a linear subspace in the linear space \(\operatorname{Mat}_{2 \times 2}(\mathbb{R})\) of all \(2 \times 2\) real matrices?
Find all linear maps \(L: \mathbb{R}^{3} \rightarrow \mathbb{R}^{3}\) whose kernel is exactly the plane \(\left\{\left(x_{1}, x_{2}, x_{3}\right) \in \mathbb{R}^{3} \mid\right.\) \(\left.x_{1}+2 x_{2}-x_{3}=0\right\}\)
Which of the following are not a basis for the vector space of all symmetric \(2 \times 2\) matrices? Why?
subspace
Coins are situated on an \(m \times m\) board. Each coin situated on the board is said to dominate all the cells of the row \((\rightarrow)\), the column \((\downarrow)\), and the diagonal \((>)\) ).
\begin{equation} \text { Let } A=\left[\begin{array}{ccc} 3 & 2 & -1 \\ 1 & 6 & 3 \\ 2 & -4 & 0 \end{array}\right] \end{equation} Then the diagonal entries of the adjoint of A are:
Can I get a single infographic that maps the entire field of mathematics?
Find the inverse of the matrix $$ A=\left(\begin{array}{rrr} 2 & 0 & 4 \\ 1 & 2 & 7 \\ 6 & 4 & 22 \end{array}\right) $$
Let \(A:=\left(\begin{array}{rrr}4 & 4 & 4 \\ -2 & -3 & -6 \\ 1 & 3 & 6\end{array}\right)\). Compute
Let \(A=\left(\begin{array}{rrr}1 & 1 & -1 \\ 1 & -1 & 2\end{array}\right)\)
What are topographic maps?
asked Jun 27, 2020 in General Knowledge by ♦MathsGee Platinum (164,236 points) | 225 views
Find the angle between a diagonal of a cube and one of its edges
There are no square matrices \(A, B\) with the property that \(A B-B A=I .\) Proof or counterexample.