Show that $ e^{A+B}=e^A e^B$ - e^ {A+B}=e^A e^B$ - Mathematics …
Apr 10, 2013 · If $A$ and $B$ are $n\\times n$ matrices such that $AB = BA$ (that is, $A$ and $B$ commute), show that $$ e^{A+B}=e^A e^B$$ Note that $A$ and $B$ do NOT have to be ...
E is a point inside square $ABCD$ such that $ECD = EDC = 15$...
Jun 18, 2020 · E is a point inside square ABCD such that $\angle {ECD} = \angle {EDC} = 15.$ Find $\angle {AEB}.$ I drew a picture for this but I don't know how to continue. Any ...
geometry - Pentagon $ (ABCDE)$ is inscribed in a circle of radius $1 ...
Jul 19, 2024 · Pentagon $ (ABCDE)$ is inscribed in a circle of radius $1$. If $\angle DEA=\angle EAB = \angle ABC$ and $m\angle CAD=60^ {\circ}$ and $BC=2AB$. Compute the area of ...
Prove that 5 lines are concurrent, and find the expression for the ...
Sep 22, 2020 · So we take the lines from centroids of $\triangle CDE, \triangle DEA, \triangle EAB$ through point $\overline {p}$ and show each of them is perpendicular to the line segment made by …
Area of Pentagon using geometry - Mathematics Stack Exchange
Apr 5, 2017 · A given convex pentagon $ABCDE$ has the property that the area of each of the five triangles $ABC$, $BCD$, $CDE$, $DEA$, and $EAB$ is unity. calculate the area of the ...
functional analysis - Operator Exponential $e^A e^B = e^ {A+B ...
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geometry - 5 triangles with the same area inside a pentagon ...
Feb 1, 2017 · A pentagon ABCDE contains 5 triangles whose areas are each one. The triangles are ABC, BCD, CDE, DEA, and EAB. Find the area of ABCDE? Is there a theorem for ...
Is there a pure geometric solution to this problem?
Here is a geometric solution provided by Dr.Shailesh Shirali: Draw a copy of triangle EAB with DA as base. That is, locate point F inside the square such that triangle FDA is congruent to triangle EAB. …
Prove $EB=EC$ and that $F,M,G,C$ are concyclic in the given figure
Dec 18, 2022 · We will make use of a couple of corollaries to the Inscribed Angle Theorem. One corollary says that a quadrilateral is concyclic iff opposite angles are supplementary. Another is …
Proof that $e^ {ab} = \left (e^a\right)^b$, using the series for $e^x$
He’s specifically trying to show it for $e$ using the series expansion.