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