 # Determinants Class 12 Notes- Chapter 4

## What is the determinant of a matrix?

When a square matrix “A” of order “n” is associated with a number, then it is titled as a determinant of the aforementioned matrix. The number involved in this square matrix can be a real number or a complex number.

In the field of mathematics, Determinants can be used for a myriad of different calculations, such as:

• Finding the area of a Triangle.
• Obtaining the solutions of linear equations in two or three variables.
• Solve Linear equations by using the inverse of a matrix
• Getting the adjoint and the inverse of a square matrix

Students can refer to the short notes and MCQ questions along with separate solution pdf of this chapter for quick revision from the links below: ### What are the properties of Determinants?

The properties of determinants have their uses in simplifying the evaluation by getting the maximum number of zeroes in a row or column. They hold true for determinants of any order. The properties of determinants are mentioned below:

1. The determinant’s value remains unchanged if the rows and columns are interchanged.
2. The sign of a determinant changes when any two rows or columns of a determinant are interchanged with each other.
3. The value of a determinant is zero when any of the rows or columns of a determinant are identical to each other.
4. For each element of a row or column which gets multiplied by a constant P, the value also gets multiplied by P.
5. The determinant obtained is a sum of two or more determinants if some or all elements of a column or a row are expressed as a sum of two or more terms.
6. When the equimultiples of corresponding elements are added, the value of the determinant remains the same whenever the operation is multiplied.
 Also Access NCERT Solutions for Class 12 Maths Chapter 4 NCERT Exemplar for Class 12 Maths Chapter 4

### Important Questions:

1. Examine the consistency of the system of equations
1. x + 2y = 2, 2x + 3y = 3
2. 2x – y = 5, x + y = 4
3. x + 3y = 5, 2x + 6y = 8
2. Using Cofactors of elements of second row, evaluate ∆=
$$\begin{array}{l}\begin{vmatrix} 5 &3 &8 \\ 2 &0 &1 \\ 1 &2 &3 \end{vmatrix}\end{array}$$
3. Find values of p if the area of a triangle is 6 sq. units and vertices are
(i) (p, 0), (6, 0), (0, 4)
(ii) (–4, 0), (0, 6), (0, p)
4. Using determinants, find the equation of the line joining (2, 3) and (4, 7)
5. Which of the following is correct
(A) Determinant is a number associated with a square matrix.
(B) Determinant is a number associated with a matrix.
(C) Determinant is a square matrix.
(D) None of these

 Algebra Square Roots Matrices Divisibility Rules

## Frequently Asked Questions on CBSE Class 12 Maths Notes Chapter 4 Determinants

Q1

### What are the uses of algebra?

Algebra helps in logical thinking and enables a person to break down a problem first and then find its solution.

Q2

### What are the uses of determinants?

The determinant is useful for solving linear equations, capturing how linear transformation change area or volume, and changing variables in integrals.

Q3

### What is a matrix format?

A set of numbers arranged in rows and columns so as to form a rectangular array is called a ‘Matrix arrangement’.