Allane v.

Online Tutor in Mathematics and Statistics

Tutor Satisfaction Guarantee

Linear Algebra

TutorMe

Question:

Explain whether T (R^2 -R) is a linear transformation. If it is a linear transformation, supply proof, and if it is not, supply a counterexample: T(a,b) = a + b

Allane v.

Answer:

Let x = (a, b) and y = (\alpha, \Beta) all elements of R^2, and k,a,b,\aplha,\Beta all elements of R. Thus, T(kx) = T(ka,kb) = (ka) + (kb) = k(a + b) = kT(a,b) = kT(x) T(x + y) = T(a + \alpha, b + \Beta) = (a + \alpha) + (b + \Beta) = (a + b) + (\alpha +\Beta) = T(a, b) + T(\alpha, \Beta) = T(x) + T(y) Thus, From the above proof, we can confirm that T is Linear.

Statistics

TutorMe

Question:

State whether the following question is true or false: A qualitative variable that categorises or describes or names an element of a population is referred to as a normal variable.

Allane v.

Answer:

True

Algebra

TutorMe

Question:

Can Cramer's Rule be applied on the following system of Linear equations: x1.cos(y) - x2.sin(y) = 1 x1.sin(y) + x2.cos(y) = -3

Allane v.

Answer:

We first determine the determinant of the coefficient matrix. The determinant is: | cos(y) -sin(y) | | sin(y) cos(y) | =cos^2 (y) + sin^2 (y) = 1 Thus, the system of equations is not equal to 0. Therefore the non-homogeneous and we can conclude that Cramer's Rule can be applied to the linear equations.

Send a message explaining your

needs and Allane will reply soon.

needs and Allane will reply soon.

Contact Allane

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.