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:

• Matrices and Determinants Study Notes PDF
• Matrices and Determinants MCQ Practice Questions PDF
• Matrices and Determinants MCQ Practice Solutions PDF

CBSE Class 12 Maths Notes Chapter 4 Determinants – Related Links

• Properties of Determinants
• Determinant of a Matrix
• Determinants For Class 12
• Determinants and Matrices
• Determinant of a Matrix
• Determinant Formula
• Determinant of a 3 x 3 matrix
• Standard Determinant
• Determinants Worksheet

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.

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

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