JEE Main Mathematics Matrices and Determinants
Any rectangular order of numbers in 'm' rows and 'n' columns is known as the matrix of order m×n. Matrices and determinants is a crucial topic for the JEE exam. These JEE matrices formulas and other important matrices and determinants formulas for JEE will help students to go through a quick revision before the exam. JEE aspirants can expect 2-3 questions on this topic.
What are Matrices?
A matrix is a set of numbers generally assembled in rows and columns.
What is a Determinant?
Determinant means the number of rows and columns, one can seize important figures about the matrix in a single number.
Matrices and Determinants Formulas
Below given are the important formulae for matrices and determinants along with matrices and determinants notes
A. Formulae for Matrices
AB ≠ BA.
(AB) C = A (BC)
Distributive law. A (B + C) = AB + AC. (A + B) C = AC + BC.
B. Formulae for Determinant
|A| = ad − bc or the determinant of A equals a × d minus b × c.
JEE Main Mathematics Matrices and Determinants Formulas
Any rectangular order of numbers in m rows and n columns is what we call a matrix of order m×n. That being said,
A = \[\begin{bmatrix} a_{11} & a_{12} & a_{13} & ... & a_{1j} & ... & a_{1n}\\ a_{21} & a_{22} & a_{23} & ... & a_{2j} & ... & a_{2n}\\ ... & ... & ... & ... & ... & ... & ...\\ a_{m1} & a_{m2} & a_{m3} & ... & a_{mj} & ... & a_{mn} \end{bmatrix}\]
Important Revision Notes on Matrices and Determinants
Two matrices are known to be equivalent when they have a similar order and each element of one is equivalent to the corresponding element of the other.
An m×n matrix A is known to be a square matrix if m = n, meaning that, number of rows = number of columns.
In a square matrix, the diagonal from the upper corner of the left-hand side to the lower corner of the right-hand side is said to be the leading diagonal or principal diagonal.
The sum of the components of a square matrix A lying along the principal diagonal is said to be the trace of A i.e. tr(A). Therefore, if A = [a\[_{ij}\]]\[_{n\times n}\], then tr(A) = \[\sum_{i=1}^{n}\] a\[_{ii}\] = a\[_{11}\] + a\[_{22}\] + a\[_{33}\]......+ a\[_{nn}\].
For a square matrix, A = [a\[_{ij}\]]\[_{n\times n}\], if all the components except that in the leading diagonal are zero (0) i.e. a\[_{ij}\] = 0, whenever i ≠ j then A will be a diagonal matrix.
A matrix A = [a\[_{ij}\]]\[_{n\times n}\] will be a scalar matrix , when a\[_{ij}\] = 0, i ≠ j = m, i = j, where m ≠ 0
FAQs on Important Matrices and Determinants Formulas for JEE
Q1. What is the Difference Between Matrices and Determinants?
Answer: In a matrix, the set of numbers are enclosed by two brackets. On the other hand, in determinants, the set of numbers are enclosed by two bars.
Matrix is most commonly used to denote the coefficients in a system of linear equations, whereas the determinant is used to solve the linear equations.
Q2. What are the Important Properties of Matrices and Determinants?
Answer: Following are the important properties associated with matrices and determinants:-
If rows are converted into columns and columns into rows, then the values of the determinant remain unchanged.
If any two rows (or columns) of a determinant are interchanged, the consequent determinant is the negative of the principal determinant.
If two rows (or two columns) in a determinant consist of corresponding elements that are equivalent, the value of the determinant will be equivalent to zero.
