How to Learn Matrix for JEE

As far as the JEE Main is concerned, Maths is an important subject. Once learned properly, students can easily score good marks in the JEE Maths exam. They should be thorough with all the formulas and theorems in Maths. Learning the formulas thoroughly will definitely help the students to save time during the exams. Maths is a subject which has a number of tricks to find the correct answer. Students should learn these tricks so that they can easily get the correct solutions. Byhearting the solutions will not work for Maths.

Let us discuss an easy and interesting topic in maths: matrix. When we arrange numbers in rows and columns, we call it a matrix. We can say that it is a rectangular array of numbers in rows and columns. Students can expect questions from matrices for any engineering entrance exam. Students are recommended to make use of each and every available resource to learn about the matrix. In this article, we will discuss matrix multiplication properties, types, addition properties, etc.

Matrix Multiplication – Properties

Following are the properties of matrix multiplication.

  • Not commutative
  • Associative
  • Distributive
  • Zero matrix multiplication
  • Multiplicative identity

Let M is a square matrix, and N be another square matrix. We can say that MN is not equal to NM. The commutative property does not satisfy here.

Matrix Addition – Properties

Following are the properties of matrix addition.

  • Commutative
  • Associative
  • Identity
  • Additive inverse

In matrix addition, the commutative property is satisfied.

Scalar Multiplication – Properties

Let M be a matrix, and N be another matrix of the same order, and p and q be two scalars, then:

  • p(M + N) = pM + pN
  • (p + q)M = pM + qM
  • p(qM) = (pqM) = q(pM)
  • (-pM) = -(pM) = p(-M)
  • tr(pM) = p tr(M), tr denotes trace of matrix.

Matrix – Types

The different types are given in the table below.

Row matrix Column matrix
Null matrix Singleton matrix
Diagonal matrix Scalar matrix
Horizontal matrix Vertical matrix
Square matrix Identity matrix
Triangular matrix Singular matrix
Non-singular matrix Symmetric matrix
Skew symmetric matrix Hermitian matrix
Skew-Hermitian matrix Idempotent matrix
Nilpotent matrix Periodic matrix
Involutary matrix Transpose matrix


Let A be a square matrix of order two having elements a11, a12, a21, a22. To calculate the determinant, we multiply a11 and a22. Then, multiply a21 and a12. Then, find the difference (a11a22 – a21a12). Students can expect questions from determinants for the JEE Main and the JEE Advanced. The determinant is an easy topic if learned properly. Students can easily score full marks on this topic if they learn the important formulas and properties. They are recommended to practice as many previous years’ questions as possible. It will help to improve their speed.

Time management is an important factor which determines the rank of the student in any entrance exam. Solving previous year’s questions and mock tests will help students to complete the exam within the stipulated time. Visit BYJU’S to download and learn previous years’ question papers, important formula PDFs, chapter-wise questions etc.

read more

Understudy Loan Solidification – Itemized Realities and Rules to Observe Prior to Applying

Understudy loans are without a doubt an incredible monetary guide for the individuals who can’t stand to subsidize their schooling. In any case, these various advances trouble understudies with overpowering obligations before long they move on from school. Composing more than one reimbursement really take a look at consistently, in the earliest reference point of a vocation, is close to inconceivable. As a rule, inability to make different installments inside the specified time-frame makes the obligations collect. Thus, loan costs continue to raise and the understudy in the long run falls into an obligation trap!

Assuming you need to keep away from the present circumstance in future, you ought to apply for an Understudy Loan Solidification, which would permit you to blend all your present advances into a solitary credit with lower financing costs and a truly adaptable reimbursement plan. In any case, prior to applying for it, there are sure significant realities that you ought to know about and a couple of rules you ought to keep:

1) Is this Choice Ideal For You?:

You ought to decide on credit combination if and provided that you are thinking that it is hard to make month to month reimbursements of your present advances on schedule. In the event that the complete equilibrium sum left on the entirety of your advances is extremely less and you are near taking care of it soon, don’t settle on union as everything will work out by any means.

2) Loan fees:

The financing cost for the united credit is assessed by taking out the normal of the loan fee of all your present advances and afterward gathering it together to the following 1/eighth of a percent. The greatest financing cost is 8.25 percent. Likewise, the financing cost is fixed and doesn’t increment with time. You can likewise utilize online home loan mini-computers to ascertain your financing cost.

3) Reimbursement Sum:

– On the off chance that you wish to diminish your month to month reimbursement sum and save large on solidifying your advances, it is important to broaden the reimbursement length of the advance. By broadening your reimbursement plan, you can even decrease your present regularly scheduled installments by 54%.

– Typically, the reimbursement time frame is 10 years, yet it tends to be stretched out to up to 30 years. Nonetheless, this generally relies upon the equilibrium sum you are combining.

– Despite the fact that broadening the reimbursement term is useful, you should pay more in interest as you would take somewhat longer to reimburse the whole advance. Nonetheless, the uplifting news here is that no pre-installment punishments are charged in the event that you decide to take care of the credit early.

4) Qualification:

Following standards ought to be met to meet the qualification prerequisites for advance solidification:

– Ought to have credits from something like two banks

– Your present understudy loans have not been solidified before

– The all out balance advance sum on all advances to be united ought to surpass $7,500

– You ought to be in your half year elegance time of your credits after your graduation or you ought to have begun making the reimbursements.

5) Advance Endorsement Interaction:

The whole advance combination process for the most part requires a month. At times, you may need to try and sit tight for over 45 days. In this manner, it is smarter to anticipate it as needs be.

6) Sorts of Advances that can be United:

– Direct Financed and Unsubsidized Advances

– Government Financed and Unsubsidized Administrative Stafford Credits

– Direct In addition to Credits and Government In addition to Advances

– Direct Solidification Credits and Government Combination Advances

– Ensured Understudy Loans

– Government Safeguarded Understudy Loans

– Government Supplemental Credits for Understudies

– Helper Advances to Help Understudies

– Government Perkins Advances

– Public Direct Understudy Loans

– Public Safeguard Understudy Loans

– Wellbeing Training Help Advances

– Wellbeing Callings Understudy Loans

– Advances for Hindered Understudies

– Nursing Understudy Loans

7) Picking the Bank:

– If all your present advances have been gained from a solitary bank, it is smarter to combine with a similar loan specialist.

– On the other hand, you can get the understudy loan solidification either through the U.S. Division of Schooling or through a monetary assistance that is enlisted in the Government Family Training Advance Program.

Consequently, with the assistance of the above realities and rules, you can get the best arrangement on an understudy loan union at the perfect opportunity from the right bank. Uniting schooling advances is a straightforward way of getting alleviation from the mind-boggling obligations, and ought to be considered to guarantee a got future.

read more

Aiding In Educational Loan Help

Financing issues are spreading in the U.S. The undergrad advance market is in emergency on account of the subprime real estate market which is adding to the Understudy Loan insufficiency. Understudy Loan banks are endeavoring to diminish the blow of this deficiency.

Financing issues are spreading in the U.S. The understudy loan market is in emergency due to the subprime real estate market which is adding to the Understudy Loan insufficiency. Understudy Loan moneylenders are endeavoring to diminish the blow of this shortfall.

Understudy loans are sold on the auxiliary market, yet financial backer interest is exceptionally low, so banks are being approached to accept more credits as separated of their money; which they are not able to do. For this situation most of the private advance banks are not able to give any longer understudy loans or combine them.

A few banks disposed of private credits to move into the government programs. The withdrawal of private credits for some monetary foundations implied a gigantic misfortune for business which securitizes private understudy loans.

What can Understudies and Guardians do in this Monetarily Diminished Market?

President Hedge has marked the “Proceeding with Admittance to Educational Loan Act”, which will extend qualification and the sum to be acquired from Government family Instruction understudy Loans, Administrative Understudy Loans and Parent Credits.

How will these help borrowers under the new rules?

The new law builds restricts on unsubsidized Stafford advances by $2,000 per year. More cash will be given to schools and state offices, which intend to benefit completely apply through your school. Qualification for In addition to credits will increment. The extraordinary thing about In addition to advances; taking an interest guardians don’t need to begin paying on the In addition to credit until a half year after the youngster graduates.

Apply for In addition to Advances while financing costs for governmentally ensured understudy loans are fixed at 6.8%, financing costs for Parent Credits for Student Understudies, or In addition to advances, are regularly higher, at present 8.5%. Guardians can get up to the full expense of school for their youngster, and In addition to credits may be more savvy than private advances.

Apply for Monetary Guide NOW: Understudies and their folks ought to talk straightforwardly with their school or college’s monetary guide office to figure out how this program will function for their school of decision.

Endeavor to get a co-endorser on a private advance in case this is conceivable. Numerous understudies don’t have a record of credit or they might have low credit injuries, following additional expenses and exorbitant loan fees. Financing costs with a co-underwriter on your understudy loans can be 7% or 8%, (with the co-endorser having great credit obviously), contrasted with 12% or 14% percent when alone on the understudy loan.

Contemplate going to a two-year school or junior college. Begin investigating the monetary guide bundles of advances and awards presented by a portion of the other, cheaper schools. Why? Since, in such a case that you there isn’t sufficient advance cash, then, at that point, the chance of going to the school of decision is thin. Consider colleges that are nearer to home, all things considered in the event that one can remain at home as opposed to a residence to save money on cost. The cash saved can be utilized for books and study material rather then food and lodging.

Despite the fact that there might be a lot of worry in the market of late. The Instruction Office says that regarding 7 million understudies will require more than $68 billion in government advances for training this coming school year. The Instruction Office will guide government assets to state-level insurance organizations, and the assets would then be dispensed straightforwardly to universities and understudies. There will be new, higher cutoff points on sums understudies can get under government instruction advance projects. On normal these cutoff points are $3,500 for first year, $4,500 for sophomore year and $5,500 every year after that. As indicated by revealed subtleties, under the new understudy loan charge, these yearly cutoff points would be expanded by $2,000.

read more