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Post a LessonAnswered on 01/03/2024 Learn CBSE - Class 12/Mathematics/Unit II: Algebra/Matrices
Kalaiselvi
Online Mathematics tutor with 8 years experience(Online Classes for 10th to 12th)
Answered on 06/04/2024 Learn CBSE - Class 12/Mathematics/Unit II: Algebra/Matrices
Sadika
The identity matrix of order n is denoted by I∩
It is a square matrix with dimensions n×nn×n where all the elements on the main diagonal (from the top left to the bottom right) are 1, and all other elements are 0.
Answered on 06/04/2024 Learn CBSE - Class 12/Mathematics/Unit II: Algebra/Matrices
Sadika
A square matrix is a matrix that has the same number of rows and columns. In other words, it is a matrix where the number of rows is equal to the number of columns.
For example, a 3×33×3 matrix and a 4×44×4 matrix are both square matrices because they have 3 rows and 3 columns, and 4 rows and 4 columns, respectively.
Square matrices are commonly encountered in various mathematical contexts, such as linear algebra, where they are used to represent linear transformations, systems of linear equations, and many other mathematical structures.
read lessAnswered on 06/04/2024 Learn CBSE - Class 12/Mathematics/Unit II: Algebra/Matrices
Sadika
To find the number of all possible matrices of order 3×33×3 with each entry being either 0 or 1, we can consider that each entry in the matrix has 2 choices (0 or 1), and there are a total of 3×3=93×3=9 entries in the matrix.
Therefore, the total number of possible matrices is 2929, because for each entry, there are 2 choices, and we multiply these choices together for all 9 entries.
So, the number of all possible matrices of order 3×33×3 with each entry being either 0 or 1 is 29=51229=512.
Answered on 06/04/2024 Learn CBSE - Class 12/Mathematics/Unit II: Algebra/Matrices
Sadika
Two matrices A=[aij]A=[aij] and B=[bij]B=[bij] are said to be equal if they have the same dimensions (i.e., the same number of rows and columns) and if each corresponding entry of matrix AA is equal to the corresponding entry of matrix BB.
Formally, two matrices AA and BB are equal if and only if:
In other words, matrices AA and BB are equal if they have the same size and if the corresponding entries in each position are equal.
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