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Online CBSE Study Material Previous year Question Papers of CBSE CBSE NCERT SOLUTIONS of Maths and Science Regular Topic-wise articles MCQs based Tests & Quizzes CBSE Sample Papers 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. → 1 2 5 Eg Rows → 9 0 1
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Columns 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 Ă— n. In above example, the order of matrix is 2Ă—3 since there are two rows and three columns. Let us take a matrix
1 5 5
2 0 7 3 9 1
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. For the practice sets of Matrix & more, click on 12 mathematics online classes.
Question: In the matrix
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Write order, the number of elements and the elements of a12,a13,a23,a32. Solution: The order of the matrix is 3Ă—3. No of elements are 3Ă—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 2Ă—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
4 9 9 16
Question: Construct a matrix A = [aij]2×2 whose elements aij are given by aij = e2ix sin jx . a11 = e2x sin x a12 = e2x sin 2x a21 = e4x sin x a22 = e4x sin 2x
Solution: For i = 1, j = 1, For i = 1, j = 2, For i = 2, j = 1, For i = 2, j = 2,
The matrix is
e sinx e sinx
e sin2x e sin2x
Question: Construct a 3×2 matrix whose elements are aij = |i – 3j| 1 5 / 2 Ans: 1 / 2 2 0 3 / 2
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