You must have learned in the earlier classes about matrix and matrices. For every square matrix, you can assign a real number. It is called the Determinant.
Determinant of matrices of order 1:
If A = [a ] be the matrix of order 1, then Determinant of A is said to be equal to a.
Determinant of matrices of order 2 ☓ 2:
For matrices with order 2, the Determinant is obtained through the multiplication of matrices.
Determinant of matrices of order 3 ☓ 3:
For matrices with order 3 ☓ 3, the Determinant is obtained by a series of steps explained in the NCERT solutions for Class 12 Maths Part 1 Chapter 4 Determinants.
Properties of Determinants :
Chapter 4, Determinants, gives us a few properties.
Property 1. If you interchange the rows and columns, the value of Determinants will not change.
Property 2. If two rows or 2 columns are interchanged, then the value of Determinants will change concerning sign.
Property 3. If two-row or columns are the same, then the value of Determinants is zero.
Property 4. If each element in matrix is multiplied by a constant k, then the value of Determinants will also be multiplied by k.
Property 5. If the sum of two terms expresses elements, then the value of Determinants will also be expressed as the sum
Area of a triangle :
As we have seen in earlier classes, the area of a triangle is half into base into height.
Here, the value of the area of the triangle is expressed as half of the value of the matrix of order 3 ☓ 3.
Exercise 4.3 has five questions based on these concepts.
For detailed and correct solutions for Exercise 4.3, you can download our NCERT Solutions for Class 12 Maths Part 1 Chapter 4 Determinants.
The importance of using NCERT Solutions for Class 12 Maths Part 1 Chapter 4- Determinants :
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