Kerala Board Plus Two Maths Chapter 4 Determinants Important Questions

Mastering mathematics requires structured practice and clear conceptual understanding. Working on each Kerala Board Plus Two Maths Chapter 4 Important Question helps students secure high marks in board examinations.

Determinants is an important unit in higher secondary mathematics. Board exam questions commonly cover finding matrix inverses, calculating cofactors, and solving systems of linear equations. Practising these core methods helps students build speed and accuracy in the Kerala Plus Two exam.

It provides targeted questions with step-by-step solutions for complete exam readiness. Students will learn how to evaluate determinants and test whether a system has a unique or trivial solution. You can also review the Kerala Plus Two Exam Pattern to plan your study schedule.

Kerala Board Plus Two Maths Chapter 4 Important Questions

Reviewing high-yield questions helps improve problem-solving speed and accuracy. Understanding the Kerala Plus Two Exam Pattern can also help students prepare effectively for the examination. Below are selected questions covering key concepts from this chapter.

Below are selected questions covering key concepts from this chapter.

Question 1: Find the area of a triangle whose vertices are (3, 8), (−4, 2) and (5, 1) using determinants.

Answer:
The area of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is:

Area = ½ × |Δ|

where Δ is the determinant of the matrix with rows [x₁ y₁ 1; x₂ y₂ 1; x₃ y₃ 1].

Substitute the coordinates:

Δ = determinant of [3 8 1; −4 2 1; 5 1 1]

Expand along the first row:

Δ = 3(2 × 1 − 1 × 1) − 8((−4) × 1 − 1 × 5) + 1((−4) × 1 − 2 × 5)

Δ = 3(1) − 8(−9) + 1(−14)

Δ = 3 + 72 − 14 = 61

Area = ½ × 61 = 30.5 square units

Hence, the area of the triangle is 30.5 square units.

Question 2: Let A = [1 1 1; −1 is not used here. The matrix is A = [1 1 1; 1 −1 −1; 1 1 −1]. Find the inverse of A.

Answer:
Matrix A has rows [1 1 1], [1 −1 −1] and [1 1 −1].

Step 1: Find |A|.

|A| = 1[(−1)(−1) − (−1)(1)] − 1[(1)(−1) − (−1)(1)] + 1[(1)(1) − (−1)(1)]

|A| = 1(1 + 1) − 1(−1 + 1) + 1(1 + 1)

|A| = 2 − 0 + 2 = 4

Since |A| ≠ 0, A⁻¹ exists.

Step 2: Find the cofactors.

A₁₁ = 2, A₁₂ = 0, A₁₃ = 2
A₂₁ = 2, A₂₂ = −2, A₂₃ = 0
A₃₁ = 0, A₃₂ = 2, A₃₃ = −2

Step 3: Find the adjoint, which is the transpose of the cofactor matrix.

adj A = [2 2 0; 0 −2 2; 2 0 −2]

Step 4: Use A⁻¹ = (1 ÷ |A|) × adj A.

A⁻¹ = ¼ × [2 2 0; 0 −2 2; 2 0 −2]

A⁻¹ = [½ ½ 0; 0 −½ ½; ½ 0 −½]

Hence, the inverse of A is [½ ½ 0; 0 −½ ½; ½ 0 −½].

Question 3: Express the matrix A = [2 −2 −4; −1 3 4; 1 −2 −3] as the sum of a symmetric and a skew-symmetric matrix.

Answer:
Any square matrix A can be written as A = P + Q, where:

P = ½(A + A′) is symmetric
Q = ½(A − A′) is skew-symmetric

Here, A′ = [2 −1 1; −2 3 −2; −4 4 −3].

Step 1: Find P.

A + A′ = [4 −3 −3; −3 6 2; −3 2 −6]

P = ½(A + A′) = [2 −1.5 −1.5; −1.5 3 1; −1.5 1 −3]

P′ = P, so P is symmetric.

Step 2: Find Q.

A − A′ = [0 −1 −5; 1 0 6; 5 −6 0]

Q = ½(A − A′) = [0 −0.5 −2.5; 0.5 0 3; 2.5 −3 0]

Q′ = −Q, so Q is skew-symmetric.

Step 3: Verify.

P + Q = [2 −2 −4; −1 3 4; 1 −2 −3] = A

Hence, A = P + Q, where P is the symmetric part, and Q is the skew-symmetric part.

Kerala Plus Two Mathematics Chapter 4 PDF Download

Students can access the complete Kerala Plus Two Maths Chapter 4 Matrices and Determinants PDF for offline preparation. This PDF contains extra practice sheets and model solutions aligned with the latest Kerala Class 12 Syllabus.

Get the verified Kerala Board Class 12 Maths Matrices and Determinants PDF to practice at your own pace. You can also find additional revision material in the Class 12 Matrices and Determinants PDF Kerala Board module. Use the Kerala Plus Two Maths Chapter 4 PDF during revision to reinforce formulas.

Preparation Strategy for Kerala Board Class 12 Maths Determinants Using Important Questions

Structured revision improves conceptual clarity and reduces calculation errors during exams. Determinant questions are step-based, so one small sign mistake can change the final answer.

Follow the points below after solving the important questions, so that you revise each method in the right order and build speed.

• Master Core Definitions: Understand minors, cofactors, and adjoint calculations thoroughly before solving complex equations.

• Practice Matrix Inverses: Solve system equations using the matrix inversion method to secure full marks in long-answer sections.

• Verify System Consistency: Check whether |A| = 0 to identify singular matrices and test for a homogeneous system or trivial solution.

• Solve Previous Papers: Practice with Kerala Plus Two Model Papers to improve speed and time management.

• Revise Linked Units: Strengthen related concepts by studying Kerala Plus Two Maths Relations and Functions.

Practising Kerala Board Plus Two Maths Chapter 4 Important Questions helps students strengthen their understanding of matrices and determinants, improve problem-solving accuracy, and prepare for board exams. Download the Kerala Plus Two Maths Chapter 4 PDF to practise additional questions with solutions and revise key concepts for better exam performance.