RD Sharma Class 12 Chapter 5 Solutions (Algebra Of Matrices)
RD Sharma Class 12 Maths Solutions Chapter 5 ‘Algebra of Matrices’ build-up from the knowledge that we had gained in class 11 about matrices. This chapter involves the revision of the previous concepts and then explains topics like properties of matrices, operations on matrices, transpose of matrices etc.
This chapter of RD Sharma Class 12 Solutions is considered essential from the prospect of CBSE board exam as there are one or two questions definitely from this topic. There are a total number of 277 questions in 7 exercises. These questions are from the basic operation of matrices like addition, subtraction, and multiplication.
The comprehensive study of Matrices has been condensed by the Instasolv experts in RD Sharma Class 12 Maths Solutions Chapter 5 – Algebra of Matrices. The solutions offered are detailed and explained step-wise to make your learning more productive and effortless. The solutions aid in identifying the mistakes and to rectify them during your revisions.
Important Topics for RD Sharma Class 12 Maths Solutions Chapter 5- Algebra of Matrices
What is the Matrix?
In a very simple language, the matrix can be considered as a rectangular box which has lots of numbers in it. These numbers are called the elements of a matrix.
Order of a Matrix:
Any matrix has a representation. Being a rectangular array of numbers, a matrix has a certain number of rows and a certain number of columns. Suppose there is one matrix with c no of column and r no of rows. Then the order of the matrix will be ‘r x c’.
Types of Matrices
- Column Matrix: A column matrix is a special type of matrix. This kind of matrix has only one element in each of the rows and only one column.
- Row Matrix: When a matrix has only one row regardless of the columns it has, it is called a row matrix.
- Square Matrix: When the order of the matrix is ‘r x r’, i.e., the number of rows is equal to the number of columns, then it looks like a square and it is called a square matrix.
There are many types of other matrices. Some of the common are scalar matrices, equal matrices, zero matrices, diagonal matrices, etc. Each of them has its own properties.
Operations on Matrices
There are three main operations of matrices that we will be focusing on in the class 12 RD Sharma Solutions for Maths. These three operations are sum, difference and multiplication. There are ways to add two matrices. When two matrices are added up, the corresponding element of the first matrix is added up with the second. While finding out the difference between the two matrices, the same process is repeated.
Multiplication in matrices is different from addition and subtraction. The first thing that needs to be considered while multiplying two matrices is that the order of the two matrices that are going to be multiplied should be the same. Suppose there are two matrices C and D. So, the elements of C in the row should be multiplied with each element in the column of the matrix D. Then once, all this is done, the sum has to be added up to find the product matrix.
Properties of Matrix Addition
The matrices follow the commutative law property while addition. This law expounds that if there are two matrices named C and D, whether you add the later first with former or vice-versa, there is no effect on the sum. There can be more than two matrices, but it won’t change the law. Similarly, matrix addition follows other properties like associative law, the law of additive identity and law of additive inverse.
Transpose of a Matrix
The transpose of a matrix means simply interchanging the rows with columns and columns with rows. Let us study it with a simple example. If there is a Matrix C with the order r x c, the transpose of the matrix C can be determined by C’. The order of matrix C’ will be c x r.
Exercise Discussion of RD Sharma Class 12 Maths Solutions Chapter 5- Algebra of Matrices
- Exercise 5.1 deals with the addition of matrices and properties and there are around 22 questions related to it.
- The second exercise, i.e., 5.2, deals with matrix multiplication and properties and has 27 questions in it.
- Exercise 5.3 has 96 problems including word problems that are based on matrix multiplication. This is one of the most important exercises in the entire book.
- Exercise 5.4 has problems on the elementary operation of matrices and has 16 questions in it.
- Exercise 5.5 has 8 questions in it. Exercise 5.6 is another major exercise with around 63 questions basically related to multiplication of the matrix and other properties.
- The last exercise consists of 45 MCQs and they are very important for the analysis of your knowledge related to matrices.
Benefits of RD Sharma Class 12 Maths Solutions Chapter 5- Algebra of Matrices by Instasolv
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