CBSE Class 12 Maths Online Classes and NCERT Solutions - Matrix

1. CBSE Class 12 Maths Online Classes- Matrix Class 12th maths: Takshila Learning objective is to impart quality education to its students. We have prepared an online course which caters to all your needs to score good marks in CBSE exams. Our online study material is unique & content is regularly updated keeping in mind the latest pattern of question paper of Board exams. You can also take our Class 12thNCERT Solutions and Question bank with detailed solutions & analysis in order to keep track with the pace of other students. We offer animated video classes for Class 12th Maths and Science. Online Classes for Class 12th includes: 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. Eg Rows → 9 0 →1 2 5 1

2. ↑ ↑ ↑ 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 × n. In above example, the order of matrix is 2×3 since there are two rows and three columns. 1 5 5 2 7 9 0 3 1 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 tothe 3rd row and 2nd column. For the practice sets of Matrix & more, click on 12 mathematics online classes. ? ? ? ? ? ? ? ? ? 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

3. 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 16? 9 Question: Construct a matrix A = [aij]2×2 whose elements aij are given by aij = e2ix sin jx . Solution: 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 ?e?? sinx e?? sin2x e??sin2x? e??sinx Question: Construct a 3×2 matrix whose elements are aij = ? ? |i – 3j|   1 5 / 2  / 1  Ans: 2 2       0 3 / 2 For more inquiries, CBSE class 12 Maths, articles, video lectures, CBSE exam alerts, Syllabus, sample papers for Class 12th, register with Takshila Learning Call us : 8800999280/8800999284