Matrices Class 12 NCERT Solution 2021

The arrangement of real numbers in a rectangular array that is enclosed in brackets as “[]” or “()” is known as a Matrix. It should be noted that matrices is the plural of the matrix. Matrix operations are used in computers, electronic physics, budgeting, cost estimation, analysis and experiments, electronic physics. They are also used in modern psychology, cryptography, genetics, industrial management, and so on. In general, an m x n matrix is matrix that has got m rows and n columns.

Order of A Matrix

In a matrix, there may be any number of rows as well as any number of columns. If there are m rows and n columns in matrix A, its order would be m x n and it would be read as an m x n matrix.

Types of Matrices

Row matrix: In a row matrix, there is the presence of just one row but any number of columns.
Column matrix: Regarding a column matrix, it has got only one column but any number of rows.
Square matrix: A square matrix has got the number of columns which is equal to the number of rows.
Rectangular Matrix: A matrix is said to be a rectangular matrix if the number of rows does not equals to the number of columns.
Diagonal matrix: If a square matrix has got all elements 0 except principal diagonal elements, it is called the diagonal matrix.
Scalar Matrix: A diagonal matrix is said to be a scalar matrix if all the elements in its principal diagonal are equal to some non-zero constant.

Let us have a look at some of the Matrices Class 12 NCERT Solution 2021 that would help you in getting some good idea about it.

Question 1: If a matrix has 24 elements, what are the possible orders it can have? What, if it has 13 elements?

Answer: The number of elements = 24

Therefore, the possible orders are as follows: 1 x 24,2 x 12,3 x 8,4 X 6,6 X 4,8 X 3,12 x 2 and 24 x 1

If it has 13 elements, then the possible orders: 13 x 1 and 1 x 13

Question 2: If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

Answer: Total number of elements in matrix = 18

Therefore, the possible orders are as follows:

E MY 1 x 18,2 x 9,3 X 6,6 X 3,9 x 2 and 18 x 1 If it has 5 elements, then the possible orders: 5 x 1 and 1 x 5

Question 3:Construct a 3 x 4 matrix, whose elements are given by:

(i) ajj = 1-3i+j1

(ii) aij = 2i – j

Answer:

The elements of matrix are: 211 = 31 – 3 + 1 = 1, 212 = 31 – 3 + 21 = = 0, 3 = 31 – 3 + 3) = 0, 2z4 = 31 – 3 + 4|

51 – 3 + 3 = 0, – 1] = 222 = 51 – 6 + 21 = 2, 223

51 – 6 + 41 = 1, 231 = 51 – 9 + 1) = 4, 232 = 31 – 9 + 21 = 033 = 51 – 9 + 31 = 3, 034 = 51 – 9 + 41 = 3,

=-1-3+

1-3 + 4

FIN-

Therefore, matrix =

oni

223 = 14 = 2 – 4 = -2, 224 = 4 – 4 = 0, 034 = 6 – 4 = 2.

(ii)Here, aii = 2i – j, therefore, the elements of matrix are: 211 = 2 – 1 = 1, 212 = 2 – 2 = 0, 013 = – 3 = -1, 221 = 4 – 1 = 3, a 3 = 031 = 6 – 1 = 5, 232 = 6 – 2 = 4, 033 = 6 – 3 = 3, 11 0 -1 -2]

Therefore, matrix = 3 2 1 0

15 4 3 2 1

Question 4: Find the value of a, b,c and d from the equation:

fa- b 2a +c]-[-1 51

L2a – b 3c + d. 10 13)

Answer: If two matrices are equal, then their corresponding elements are also equal.

Therefore a – b = -1 … (1)

2a – b = 0…..2

2a + c= 5 ….. (3)

3c + d = 13 …..(4)

Solving equation (1) and (2), we get

a = 1, b = 2

Putting the value of a in equation (3), we get

c = 3

Putting the value of c in the equation (4), we get

d = 4

Question 5:The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is:

(A) 27

(B) 18

(D) 512

Answer: The total number of elements in a matrix of order 3 x 3 = 9 If each entry is 0 or 1, then total number of permutation for each element = 2 Therefore, the total permutation for 9 elements = 29 = 512 Hence, the option (D) is correct.

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