Class 12 RS Aggarwal Chapter-7 Adjoint and Inverse of a Matrix Solutions - Free PDF Download
FAQs on RS Aggarwal Class 12 Solutions Chapter-7 Adjoint and Inverse of a Matrix
1. Define Matrices, and Where do we see it in the Real World?
Matrices are used in our daily world more than one can think. We get to see its usage in front of our eyes every day when we are at work or in the university studying complex topics. Graphic software such as Adobe’s Photoshop and Premiere Pro uses matrices to process the linear transformations used to render the images. A square matrix can easily represent the transformation of the geometric object.
Also, several IT companies use matrices in their data structures to track down the user information, perform the search of queries and manage their database. You can find out the usage of matrices not only in tech but even in geology matrices are used to learn about seismic surveys. Lastly, they are used to map out real-world data such as the population of a specific region, infant mortality rate, etc. these are some of the real-world use cases of matrices.
2. What are Adjoints?
An adjoint of a given matrix is said to transpose the cofactor matrix of a given matrix. Any given matrix that can be written as (A) will have its adjoint, denoted as adj (A). Also, when you multiply the matrix with its Inverse, you will get the identity matrix represented by A-1. You can even say an identity matrix to be a unit matrix where the size of both the matrix A and its Inverse is (n x m) square matrix that needs to have ones on one of its diagonal and zeros present elsewhere.
3. What are Different Types of Matrics?
There are six different types of matrices to be precise: Square matrix, Symmetric matrix, Triangular matrix, Diagonal matrix, Identity matrix, and Orthogonal matrix. From these six matrices, there are only a few matrices that are used commonly. These matrices are Square matrices in which the number of rows is equal to the number of columns. On the other hand, a matrix that doesn’t have an equal number of rows and columns will be considered a rectangular matrix.
Likewise, the symmetric matrix is also a square matrix in which the top right triangle is the same as the bottom left triangle. The Diagonal matrix in which the values present at the outside of the main diagonal have zero value and the main diagonal is taken from the top left of the matrix to the bottom right. Lastly, there’s an identity matrix that doesn’t change any of its vectors when multiplied.
4. What are the different theorems explained in chapter 7 of Class 12 RS Aggarwal?
Chapter 7 RS Aggarwal of class 12 mathematics explains four different theorems to the students. These theorems help explain the concepts of the chapter better to the students. The four theorems are as follows:
1. Theorem 1:
If A is any square matrix of order n, then A (Adj A) is equal to (adj A) A, which is equal to A I, where ‘I’ is the identity matrix of order n
2. Theorem 2:
AB and BA are non-singular matrices of the same order if A and B are non-singular matrices of the same order.
3. Theorem 3:
A and B are square matrices of the same order, then the determinant of the product of matrices is equal to the product of their determinants, i.e.,
AB=IAI IBI
4. Theorem 4:
If A is a non-singular matrix, then square matrix A is invertible as well.
5. How do I prepare for Class 12 Chapter 7 For my board exams?
Students have to work hard in class 12 to score high marks in the board exams. They have not only to prepare for the board exams but also for the competitive exams. Therefore, it is important to understand the concepts properly. Students can prepare class 12 chapter 7 from the RS Aggarwal Class 12 Solutions Chapter 7 that is available on Vedantu.