Matrices

This post shall deal with Matrices as a topic for preparation of JEE Advanced and JEE Mains. The nature of questions and the important topics shall also be discussed.

Importance

Yearly Trend

The trend in the question papers in the past few years clearly suggests that Matrices is one of the major topics as far as JEE perspective is concerned. It is a topic of huge importance, carries a lot of marks and can fetch you a lot of marks if you get things right.

The trends show that up to 3 questions from this topic were asked in JEE Advanced in 2011. And in almost all the other years, 1 or 2 questions have been asked, making this a topic to be heavily focused on. And these questions may appear in Mix and Match type or Comprehension type, which carry a lot of marks. In JEE Mains also, the trend clearly shows that at least 1-2 questions are to be expected. All in all, It is a heavily scoring topic.

Topics

A high weightage of marks obviously means that a wide variety of
questions can be asked.

Matrices is a topic in which questions can be framed by combining matrices with a lot of other topics like determinants or complex numbers. So, if not directly, matrices still has a role to play in a lot of questions.

From Matrices itself, the most commonly asked questions are about the properties of matrix, related to its transpose or inverse, or its nature being symmetric or skew-symmetric. All the elements may or may not be mentioned and the solution will be demanded in the form of a matrix. Certain transformations will have to be performed to get the answer. Comprehensive type questions remaining very frequently asked.

Another common type of question asked is related to matrix with entries as only 0 and 1 (or unit matrix), where conditions are mentioned and solutions are demanded using properties.
The questions in which matrices are used as a tool to solve a system of equations is also important.

The most important topic when it comes to matrices is solving a system of equations. A system of equations is mentioned, which is then converted into a matrix form, which is then solved by using determinants, using the Cramer’s rule. The nature of the roots is generally asked which can be easily found out and answered.

All in all, it’s a very important topic and requires a genuine effort, but once done, reaps high reward.