TutorMe homepage
Subjects
PRICING
COURSES
SIGN IN
Start Free Trial
Evren Z.
The Dr. of Mathematics
Tutor Satisfaction Guarantee
Linear Algebra
TutorMe
Question:

Prove that the following matrix $$A$$ is invertible. $$\begin{bmatrix}10 & 3 \\ 4 & 5\end{bmatrix}$$.

Evren Z.
Answer:

The matrix $$A$$ is invertible $$\Leftrightarrow $$ $$det(A)\neq 0 $$. So, $$det(A)=50-12=38\neq 0\Leftrightarrow A$$ is invertible.

Geometry
TutorMe
Question:

Write the equation $$x^{2}+y^{2}-3x+4y+4=0$$ in standard form.

Evren Z.
Answer:

Completing the square for the $$x$$-terms with $$\frac{9}{4}$$ and for the $$y$$-terms with 4, $$ \left( x^{2}-3x+\frac{9}{4} \right)+\left ( y^{2}+4y+4 \right)=-4+\frac{9}{4}+4$$. Factoring each group of terms gives rise to $$\left ( x-\frac{3}{2} \right )^{2}+\left ( y+2 \right )^{2}=\left ( \frac{3}{2} \right )^{2}$$.

Calculus
TutorMe
Question:

Give the geometrical interpretation of the integral $$\int_{0}^{1}x^2dx$$.

Evren Z.
Answer:

Keep in mind that there is a direct link between geometry and calculus in terms of evaluating the definite integrals. The integral gives us the area bounded by the curve $$y=x^{2}$$ , the $$x-axis$$ and the line $$x=1$$.

Send a message explaining your
needs and Evren will reply soon.
Contact Evren
Ready now? Request a lesson.
Start Session
FAQs
What is a lesson?
A lesson is virtual lesson space on our platform where you and a tutor can communicate. You'll have the option to communicate using video/audio as well as text chat. You can also upload documents, edit papers in real time and use our cutting-edge virtual whiteboard.
How do I begin a lesson?
If the tutor is currently online, you can click the "Start Session" button above. If they are offline, you can always send them a message to schedule a lesson.
Who are TutorMe tutors?
Many of our tutors are current college students or recent graduates of top-tier universities like MIT, Harvard and USC. TutorMe has thousands of top-quality tutors available to work with you.