Xam Idea Class 12 Maths Chapter 3 Solutions: Algebra Of Matrices
Xam Idea 12 Maths Solutions for Chapter 3 ‘Algebra of Matrices’ is one of the popular and most effective sources for exercise solutions of this chapter for Class 12 board exams. Scoring full grades in mathematics would be simple if you take the right route and make those fundamentals clear throughout the discipline. This chapter of Xam Idea Solutions will introduce different operations of matrices such as addition, subtraction, multiplication, and division. Here you will learn to apply different rules of the algebra of matrices along with the different types of matrices such as identity matrix, row matrix, column matrix, square matrix and a diagonal matrix.
Xam Idea Class 12 Maths Solutions for the algebra of Matrices comprises a total of 50 questions and has been categorized into three sets of questions, namely Very Short questionnaire, Short Questions, and Long Answer Type Questions respectively. We have provided complete solutions for these exercises in an easy to understand language. Our solutions will help you learn the basic or central idea of applied mathematics that is further revolving around linear algebra. You will be solving questions related to finding transpose of matrices, symmetric and skew-symmetric matrices, product matrix, and invertible matrices.
Xam Idea Class 12 Maths book solutions by our subject matter experts include 100% accurate solutions based on the latest CBSE Class 12 Maths syllabus. These Xam Idea Class 12 solutions are as per the latest CBSE exam format. Each exercise has been thoroughly discussed for the benefits of the students. The main topics of the Xam Idea Class 12 Maths solutions for Algebra of Matrices are given here so that you can understand the chapter’s concepts thoroughly.
Important Topics of Xam Idea Class 12 Maths Solutions Chapter 3: Algebra of Matrices
- This chapter is believed to be an important concern in the basic arithmetic, whether it’s for your Class 12 board exams or numerous different competitive exams. Questionnaires are often raised in your examinations from this chapter and you need to work over for every concept. Let us study a few of the important concepts along with definitions associated with the angle of matrices.
- Algebra of matrices is a mathematical branch that deals with feature space vectors among multiple dimensions. The invention of matrix algebra has come due to the extreme n-dimensional planes existing in our coordinates space.
- A matrix is the sequence of numbers, expressions or symbols in an array of rectangles. The structure is achieved in horizontal rows and vertical columns, with an arrangement of several rows and x number of columns. Each pair of points inside a three-dimensional space represents a particular equation with more than one solution.
- Linear algebra is an analysis of linear combinations. It is the study of vector spaces, lines, and planes, and even some of the mappings used to conduct linear transformations. It incorporates vectors, matrices, as well as linear functions. It is an investigation of linear sets of equations and heir transformational properties.
- Algebra of matrices includes different operations of matrices. They are Addition, subtraction, multiplication, etc.
Addition / Subtraction of Matrices
Two matrices may be added/subtracted if the number of rows and columns both of matrices is equivalent or the order of the matrices is similar.
Under addition/subtraction, every component of the very first matrix is added/subtracted from the components contained in the second matrix.
Multiplication of Matrices
Two ways matrix multiplications:
Scalar Multiplication – Multiplication of scalar amounts to the matrix. Each component within the matrix must be multiplied by a scalar quantity to establish a new matrix.
Multiplication of a matrix with yet another matrix: both matrices may be combined if the number of columns in the very first matrix is equivalent to the number of rows in the second matrix.
Considering the 2 matrices as (M1 & M2), in order of “m1×n1”, and” m2×n2” The matrices can be combined and then only if n1 = m2
Above matrices satisfy the multiplication condition; therefore it is possible to multiply these matrices. The resulting matrix generated by multiplying two matrices is the sequence of m1 X n2, where m1 is the number of rows in the first matrix, and n2 is the number of columns in the second matrix.
Law of the Algebra Matrix:
The algebra of the matrix meets some laws for addition and multiplication. Let’s consider that A, B, and C are three different square matrices. A ‘is the transposition, and A-1 is the exact opposite of A where I is an identity matrix, and R = real number.
Laws of Algebra of Matrices
- A+B = B+A →Commutative Law Addition
- A+B+C = A +(B+C) = (A+B)+C →Associative law addition
- ABC = A(BC) = (AB)C →Associative law multiplication
- A(B+C) = AB + AC →Distributive law matrix algebra
- R(A+B) = RA + RB
Some other Rules for Transposition of Matrices
- (A’)’ = A
- (A+B)’ = A’+B’
- (AB)’ = B’A’
- (ABC) = C’B’A’
The Inverse Rules within Matrices
- AI = IA = A
- AA-1 = A-1A = I
- (A-1)-1 = A
- (AB)-1 = B-1A-1
- (ABC)-1 = C-1B-1A-1
- (A’)-1 = (A-1)’
Types of Matrices:
- Row Matrix:
A row matrix contains just one row with several columns.
Example :
A = [-1/2 √5 2 3]
This row matrix is in order of 1 × 4.
A = [a_{ij}]_{1xn} is a row matrix in order of 1 × n.
- Column Matrix :
The column matrix contains just one column with a variety of rows. The matrix is assumed to be a column matrix if there is only one column.
Example:
It is a column matrix of order m × 1.
Square Matrix:
A matrix where the number of rows is equivalent to the number of columns is considered as a square matrix. Thus, m × n matrix represents a square matrix whenever “m = n” and it is of ‘n’ order.
Example:
Here, the square matrix is in order of 3.
Rectangular Matrix:
A matrix defined as a rectangular matrix because of the number of rows not equivalent to the number of columns.
Example:
The matrix is in order of 4 × 3.
Diagonal matrix:
A square matrix B = [b_{ij}] m × m represents a diagonal matrix wherein all non-diagonal elements equal to zero and matrix
“B” = [b_{ij}]_{mxm} = diagonal matrix.
Here, b_{ij} = 0, and i ≠ j.
Example:
This is a diagonal matrix with an order of 1, 2, 3, respectively.
Exercise Discussion of Xam Idea Class 12 Maths Solutions Chapter 3: Algebra of Matrices
Within Xam Idea Class 12 Mathematics solutions Chapter 3 comprises 50 different problems sorted out in three different types. Will see what kind of problems you will get in this chapter alongside what you will understand from them
Very Short Type Questions
In this section, you will have 24 total questions. These are quite easy examples to solve. You only need a little bit of close contact in matrix rules to find solutions. Some other questions will ask you to Match the given matrices, find the value of x in the equations, and write the order of the product matrix.
Short Type questions
There are 12 questions in this section that are divided into two parts. Part one has 8 relevant questions on symmetric and square matrices, application of addition matrix formula. The next part consists of 4 questions that are based on the equality of the matrix. here you will be asked to find the value of “x”.
Long Answer Type Questions
This segment has 14 total problems, including a mixture of 4 and 6 marks questions. You need to be cautious while you apply different formulas to find your symmetric matrix solutions. It uses terms such as skew symmetry, matrix identification of order 2 and sum of symmetry. The last 6 questions are quite lengthy to solve. These are reasoning questions based on the combination of the sum of symmetric and skew-symmetric.
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- Xam Idea Class 12 Maths Solutions are created by an experienced self-study and a professional group of subject matter experts who have extensive expertise, presenting the latest CBSE syllabus.
- Our Xam Idea solutions will clear all your doubts and they include step-by-step responses to the problems in the Xam Idea Class 12 Maths book.
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- You can use these Xam Idea Class 12 Maths Solutions without any fee or cost. The easy-to-understand vocabulary and well-structured style are likely to help you plan for the upcoming Class 12 board exams.