Currently Empty: $0.00
2.Matrix Operations
Class 12 • Mathematics • NCERT
Matrix Operations
[ Embed Your Video Lecture Here ]
This lesson explains basic matrix operations such as addition, subtraction, and scalar multiplication as prescribed by NCERT Class 12. These operations form the foundation for advanced matrix concepts.
Lesson Objectives
- Understand matrix addition and subtraction.
- Learn scalar multiplication of matrices.
- Apply conditions for matrix operations.
- Solve NCERT exam-type questions.
1. Addition of Matrices
Two matrices can be added only if they have the same order.
If A = [aᵢⱼ] and B = [bᵢⱼ], then A + B = [aᵢⱼ + bᵢⱼ]
Example:
[1 2] + [3 4] = [4 6]
2. Subtraction of Matrices
Subtraction of matrices is possible only when both matrices are of the same order.
A − B = A + (−B)
Example:
[5 6] − [2 1] = [3 5]
3. Scalar Multiplication
When each element of a matrix is multiplied by a number, the operation is called scalar multiplication.
If k is a scalar and A = [aᵢⱼ], then kA = [k·aᵢⱼ]
Example:
2 × [1 3] = [2 6]
4. Important Properties (NCERT)
• A + B = B + A (Commutative)
• (A + B) + C = A + (B + C) (Associative)
• k(A + B) = kA + kB
• (k + l)A = kA + lA
• (A + B) + C = A + (B + C) (Associative)
• k(A + B) = kA + kB
• (k + l)A = kA + lA
5. Important NCERT Notes
• Matrix addition is not defined for different orders
• Scalar multiplication is always defined
• Zero matrix acts as additive identity
• Scalar multiplication is always defined
• Zero matrix acts as additive identity
Practice Questions (NCERT)
- When can two matrices be added?
- Define scalar multiplication of a matrix.
- Find A + B if A = [1 2] and B = [3 4].
- Find A − B if A = [5 7] and B = [2 3].
- Find 3A if A = [2 1].
- Is matrix addition commutative?
- Is matrix subtraction commutative?
- What is the additive identity in matrices?
- Can matrices of different orders be subtracted?
- Is this topic part of NCERT Class 12 syllabus?
✅ Show Answer Key
- When they have the same order
- Multiplying each element by a scalar
- [4 6]
- [3 4]
- [6 3]
- Yes
- No
- Zero matrix
- No
- Yes
© Aviate Learning – Matrices (NCERT Class 12)