CBSE & NCERT Solutions for class 12 maths Matrix

Matrix: A matrix is an ordered array of numbers (or functions). The numbers (or functions) are called the elements or the entries of the matrix.

The horizontal lines of elements are said to form rows of the matrix and the vertical lines of elements are said to form columns of the matrix.

In this example, we have two rows and three columns.

Order of a Matrix: A matrix having m rows and n columns are called a matrix of order m × n.

In above example, the order of matrix is 2×3 since there are two rows and three columns.

Let us take a matrix

The order of this matrix is 3×3.

In general, we use the notation [a_ij]_m×n to indicate a matrix of order m × n.

Here i= 1,2,….,m and j= 1,2,…,n.

Here a₁₁indicates the element corresponding to the 1^st row and 1^st column.

Similarly, a₃₂means element corresponding to the 3^rd row and 2^nd column.

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Question: In the matrix

Write order, the number of elements and the elements of a₁₂,a₁₃,a₂₃,a_32.

Solution: The order of the matrix is 3×3.

No of elements are 3×3=9.

a₁₂= element corresponding to 1^st row and 2^nd column ie 6

a₁₃= element corresponding to 1^st row and 3^rd column ie 5

Similarly a₂₃= 0 and a₃₂=5.

Question: Construct a 2×2 matrix whose elements are a_ij= (i + j)²

Solution: Here there are two rows and two columns

Put i = 1 and j = 1

a₁₁ = (1+1)² = 4

Now put i = 1 and j = 2

a₁₂ = (1+2)² = 9

a₂₁= (2+1)² = 9

a₂₂= (2+2)² = 16

So the matrix is

Question: Construct a matrix A = [aij]_2×2 whose elements a_ij are given by

a_ij = e^2ixsin jx .

Solution:

For i = 1, j = 1, a₁₁ = e^2x sin x

For i = 1, j = 2, a₁₂ = e^2x sin 2x

For i = 2, j = 1, a₂₁ = e^4x sin x

For i = 2, j = 2, a₂₂ = e^4x sin 2x

The Matrix is

Question: Construct a 3×2 matrix whose elements are a_ij= |i – 3j|

Ans:

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