ICSE Solutions for Class 10 Mathematics – Matrices

ICSE Solutions for Class 10 Mathematics – Matrices

ICSE Solutions for Class 10 Mathematics – Matrices

Formulae

Addition of Matrices: Let A and B be two matrices each of order m × n. Then their sum A + B is a matrix of order m × n and is obtained by adding the corresponding elements of A and B.

  

Properties of Matrix Addition:

1. Matrix addition is commutative

i.e., A + B = B + A

2. Matrix addition is associative for any three matrices A, B and C.

A + (B + C) = (A + B) + C.

3. Existence of identity.

A null matrix is identity element for addition.

i.e., A + 0 = A = 0 + A.

4. Cancelation laws hold good in case of matrices.

A + B = A + C ⇒ B = C.

Subtraction of Matrices:

For two matrices A and B of the same order, we define

A – B = A + (- B).

  

Properties of Matrices Multiplication

1. Matrix multiplication is not commutative in general for any two matrices AB ≠ BA.

2. Matrix multiplication is associative

i.e., (AB) C = A (BC) when both sides are defined.

3. Matrix multiplication is distributed over matrix addition

i.e., A (B + C) = AB + AC

(A + B) C = AC + BC.

4. If A is an n × n matrix then

InA = A = AIn

5. The product of two matrices can be the null matrix while neither of them is the null matrix.

Determine the Following

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

  

Prove the Following