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QUESTION BANK mathematics( MATRICES)
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THIS PDF CONTAINS QUESTION BANK OF CLASS 12TH CHAPTER MATRICES ALONG WITH THE ANWER KEY AT THE BOTTOM
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MatricesQUICK RECAP
MATRIX
8 A matrix is any rectangular array of numbers X Identity or Unit Matrix : A square matrix is
or functions in m rows and n columns within said to be identity matrix if all its diagonal
brackets. entries are equal to 1 and rest are zero.
A matrix of m rows and n columns is usually X Zero or Null Matrix : A matrix whose all the
written as elements are zero.
a11 a12 ......... a1n EQUALITY OF MATRICES
a a22 ......... a2n
A = 21 8 Two matrices are said to be equal, if their
am1 am2 ......... amn order is same and their corresponding
m×n
elements are also equal.
The above matrix is also represented by
A = [aij]m×n or, A = [aij]
Order of a Matrix
X A matrix having m rows and n columns has
order m×n.
Types of Matrices
X Row Matrix : A matrix having only one row.
X Column Matrix : A matrix having only one
column.
X Square Matrix : A matrix in which number
of rows is equal to the number of columns.
X Diagonal Matrix : A square matrix whose all
the non-diagonal elements are zero.
1 0 0
Ex. A = 0 2 0 is a diagonal matrix and
0 0 3
it can also be written as A = diag (1 2 3)
X Scalar Matrix : A diagonal matrix in which
all the diagonal elements are equal.
, OPERATIONS ON MATRICES
Operations Definition Properties
Addition of two Let A and B be two (i) Commutative Law : For any two matrices A &
Matrices matrices each of order B, A + B = B + A
m × n. (ii) Associative Law : For any three matrices A, B and
Then, A + B = [aij + bij] C, A + (B + C) = (A + B) + C
for i = 1, 2, ..., m and (iii) Existence of Additive Identity : For any matrix
j = 1, 2, ..., n A, if there exists a zero matrix O such that A + O
= A = O + A. Then O is called additive identity.
(iv) Existence of Additive Inverse : For any matrix A,
if there exists a matrix (–A) such that A + (–A) = O
= (–A) + A. Then (–A) is called additive inverse of A.
Mu l t i p l i c at i o n Let A be a matrix of order Let A and B be two matrices each of order m×n.
of a Matrix by a m × n. Then, for any scalar Then, for any scalars k and l, we have
Scalar k, kA = [k ⋅ aij]m × n (i) k(A + B) = kA + kB
(ii) (k + l) A = kA + lA
Multiplication of Let A and B be any two (i) Multiplication of two matrices is not commutative
two Matrices matrices of orders m × n i.e., AB ≠ BA.
and n × p respectively. (ii) Associative Law : For any three matrices A, B, and C
Then AB = C = [cik]m×p • (AB)C = A(BC)
n (iii) Distributive Law : For any three matrices A, B and C,
where cik = ∑ air brk • A(B + C) = AB + AC
r =1
• (A + B)C = AC + BC
(iv) Existence of Multiplicative Identity : For any
square matrix, there exists a matrix I such that
AI = A = IA, where I is called the identity matrix.
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