Matrices OP Malhotra S.Chand Class-10 ICSE Maths Solutions Ch-8

Matrices OP Malhotra S.Chand Class-10 ICSE Maths Solutions Ch-8.  We Provide Step by Step Answer of Exe-8 Banking with Self Evaluation and Revision of S Chand OP Malhotra Maths . Visit official Website CISCE  for detail information about ICSE Board Class-10.

Matrices OP Malhotra S.Chand Class-10 ICSE Maths Solutions Ch-8


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 video concept 1

 video concept 2

Exe-8(a),

Exe-8(b),

Exe-8(c),

Self Evaluation And Revision


Exe-8

Matrices OP Malhotra S.Chand Class-10 ICSE Maths Solutions Ch-8

Introduction:

The knowledge of matrices is necessary in various branches of mathematics. Matrices are one of the most powerful tools in mathematics. This mathematical tool simplifies our work to a great extent when compared with other straight forward methods. The evolution of concept of matrices is the result of an attempt to obtain compact and simple methods of solving system of linear equations. Matrices are not only used as a representation of the coefficients in system of linear equations, but utility of matrices far exceeds that use. Matrix notation and operations are used in electronic spreadsheet programs for personal computer, which in turn is used in different areas of business and science like budgeting, sales projection, cost estimation, analysing the results of an experiment etc. Also, many physical operations such as magnification, rotation and reflection through a plane can be represented mathematically by matrices. Matrices are also used in cryptography. This mathematical tool is not only used in certain branches of sciences, but also in genetics, economics, sociology, modern psychology and industrial management.

Matrices:

A rectangular array of m x n numbers (real or complex) in the form of m horizontal lines (called rows) and n vertical lines (called columns), is called a matrix of order m by n, written as m x n matrix. Such an array is enclosed by [ ] or ( ).

Important Formulas for Matrices 

If A, B are square matrices of order n, and In is a corresponding unit matrix, then

(a) A(adj.A) = | A | In = (adj A) A

(b) | adj A | = | A |n-1 (Thus A (adj A) is always a scalar matrix)

(c) adj (adj.A) = | A |n-2 A

(e) |adj\,(adj.A)|=|A{{|}^{{{(n-1)}^{2}}}}

(f) adj (AB) = (adj B) (adj A)

(g) adj (Am) = (adj A)m,

(h) adj (kA) = {{k}^{n-1}}(adj. A) ,k\in R

(i) adj\left( {{I}_{n}} \right)={{I}_{n}}

(j) adj 0 = 0

(k) A is symmetric ⇒adj A is also symmetric

(l) A is diagonal ⇒adj A is also diagonal

(m) A is triangular ⇒adj A is also triangular

(n) A is singular ⇒| adj A | = 0

Note:

(a) The matrix is just an arrangement of certain quantities.

(b) The elements of a matrix may be real or complex numbers. If all the elements of a matrix are real, then the matrix is called a real matrix.

(c) An m x n matrix has m.n elements.


Exe-8(a),

Matrices OP Malhotra S.Chand Class-10 ICSE Maths Solutions Ch-8

Question 1:

Write down the order of each matrix given below and the number of elements in each :

……………….

Question 2:

Classify the following matrices as equal or not equal.

…………………..

Question 3:

…………………..

………………….

…………………..

Question 10:

(i) Three pupils in …………………….. 76, 88, 77.

(ii) If the price of a record …………… prices matrix.


Exe-8(b),

Matrices OP Malhotra S.Chand Class-10 ICSE Maths Solutions Ch-8

Question 1:

Given matrix A = ……………….. each of the following cases :

(i) X = A + B + C

………………….

Question 2:

…………………..

…………………..

…………………..

Question 18:

Solve for A and B, when

2A + b = …………………..


Exe-8(c),

Matrices OP Malhotra S.Chand Class-10 ICSE Maths Solutions Ch-8

Question 1:

If A = ……………. each of the following :

(a) AB, …………………….

(b) A², ……………

(c) A(BC), …………………….

Question 2:

……………………..

………………………

……………………….

Question 25:

If A ………………… write down the matrix AB. ……………. give reasons.


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Matrices OP Malhotra S.Chand Class-10 ICSE Maths Solutions Ch-8

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