CBSE Class 12 Maths Online Classes- Matrix
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In this article, ‘Matrix’ from CBSE Class 12th Maths is being discussed.
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 [aij]m×n to indicate a matrix of order m × n.
Here i= 1,2,….,m and j= 1,2,…,n.
Here a11 indicates the element corresponding to the 1st row and 1st column.
Similarly, a32 means element corresponding to the 3rd row and 2nd column.
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Question: In the matrix
Write order, the number of elements and the elements of a12,a13,a23,a32.
Solution: The order of the matrix is 3×3.
No of elements are 3×3=9.
a12= element corresponding to 1st row and 2nd column ie 6
a13= element corresponding to 1st row and 3rd column ie 5
Similarly a23= 0 and a32 =5.
Question: Construct a 2×2 matrix whose elements are aij = (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 aij are given by
aij = e2ix sin jx .
For i = 1, j = 1, a11 = e2x sin x
For i = 1, j = 2, a12 = e2x sin 2x
For i = 2, j = 1, a21 = e4x sin x
For i = 2, j = 2, a22 = e4x sin 2x
The Matrix is
Question: Construct a 3×2 matrix whose elements are aij = |i – 3j|