Important Questions for Class 12 Maths Chapter 4 – Determinants

1) Determine maximum value of

Ans –

Upon expanding along the first row, R₁ we get

Ans – Given a singular matrix A

3) Find the value of

Ans –

Taking the common factor of 4 from C₁ and (a + b + c) from C₂, we obtain

4) Calculate the value of

Ans –

Since R₁ and R₃ are identical
Δ = (x + y + z)(-3) × 0
= 0

5) Prove the following by using the properties of determinants

Ans –

= (a + b) (b + c) [1 {2(c + a) – 0}]
= 2(a+b)(b + c) (c + a) = RHS

6) Prove the following by using the properties of determinants

Ans –

= (3xyz + xy + yz + zx)[1 – {0 – (-9)}]
= 9(3xy + xy + yz + zx)
= RHS
⇒ Hence Proved.

7) By utilizing the properties of determinants, show that

Ans –

Upon expanding along C₃, we obtain
LHS = 4 (a + 2) – 4a – 10
= 4a + 8 – 4a – 10
= – 2 = RHS
⇒ Hence proved.

NCERT Questions for Class 12 Maths Chapter 4 – Determinants

Within the field of mathematics, determinants are fundamental in many mathematical ideas and computations. For students in class 12, mastery of advanced subjects and problem-solving depends on a knowledge of determinants. Practicing relevant determinant questions is a great approach to confirm knowledge and increase confidence in this field.

Importance of Determinants in Class 12:

• Determinants are fundamental in class 12: basis of linear algebra, an area of mathematics dealing with linear equations and related transformations. Solving systems of linear equations and learning vectors in space depend on an awareness of determinants.
• Determinants find application in geometry to ascertain the features of geometric forms and volumes. For example, determinants allow one to find the area of a triangle, therefore highlighting their useful nature in many geometric challenges.
• Determinants are strongly connected to the inversion of matrices. Students can find whether a matrix is invertible or singular by computing the determinant of a square matrix, therefore guiding their additional study of matrix operations and transformations.