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### Question of the Day: Linear Algebra

The trace of a singular matrix is 0.

Which of the following *must* be true of the eigenvalues of as a result?

One eigenvalue is 0; the other two are each other's complex conjugate.

One eigenvalue is 0; the other two are each other's additive inverse.

One eigenvalue is 0; the other two are each other's multiplicative inverse.

The only eigenvalue is 0.

0 is not an eigenvalue.

Linear Algebra is a branch of algebra that requires two dimensional reasoning skills in a wide range of multi-dimensional concepts. Though there are four “main” concepts, there are sub-topics within those that may take fine-tuning to fully grasp. You can take advantage of free Varsity Tutors’ Learning Tools to work alongside your coursework or serve as a suitable study aid. Whether you need to assess your preparation before a test, or you want to refresh your memory of eigenvalues, eigenvectors, or identity matrix, you can use a variety of free Linear Algebra math practice materials from this site. One valuable tool is the Question of the Day, which grants you the ability to practice your math skills on a regular basis.

The Linear Algebra Question of the Day may cover any of the different concepts that you need to be strong in to pass the class. Consider using the daily question as a spontaneous chance to flex your skills, test to see your knowledge of the concept, or to see your development in it. You will be asked questions concerning the criteria for uniqueness and consistency, row operations, matrix-matrix product, gradients of the determinant, eigenvalues as optimization, the hessian, gradients and hessians of quadratic and linear functions, inverses, transpose, and quadratic forms and positive semidefinite matrices. At the essence, Linear Algebra revolves around understanding matrix transformations, vector to vector mapping, thinking in terms of spaces, and exploring coordinate systems.

With the Question of the Day, your mind is kept engaged. Rather than learning through memorization, you are truly tested through the randomization of the questions. These are pulled directly from Linear Algebra test review materials, and are formatted to simulate the real tests you will be taking throughout the school year. With each question that you answer, your mind is set to focus on specific concepts, encouraging flexible thinking and letting you test your mathematical skills. When you answer, you are given a detailed analysis of your knowledge in the concept. Consider the amount of time it took you to answer the question, your general record within the concept, and your percentile. You are able to look at a detailed breakdown of the daily question to see where things went wrong, or why the answer is what it is.

With the Learning Tools, you can choose to use the Question of the Day on its own, or in conjunction with other tools. These all work well together to provide free daily Linear Algebra practice. The free practice tests allow you to identify your weak areas, which can tighten your study focus on the more important concepts, as well as assess your preparation for upcoming exams. The flashcards offer a fun way to review specific concepts, and are particularly valuable before a test. The Learn by Concept tool offers you a means of delving into the base of the concepts, giving you a total review of the information.

When it comes to studying Linear Algebra, it can be ideal to have materials that can work with your coursework. Varsity Tutors’ Learning Tools offer you flexible study options that can be accessed anytime, whether you’re at school or studying at home.

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