NCERT Exemplar Class 12 Maths Chapter 3 Solutions: Matrices
NCERT Exemplar Class 12 Maths Solutions for Chapter 3 are designed as per the latest CBSE syllabus. The NCERT Exemplar Class 12 Maths has many exemplar problems around the concept of matrices and matrix algebra. Other exemplar problems in the chapter include different types of matrices and how you equate 2 matrices, matrix addition, matrix scalar multiplication, matrix transpose, symmetric and skew-symmetric matrix, invertible matrices and how to find the inverse of a matrix using elementary transformations.
NCERT Class 12 Maths Exemplar Chapter 3 has a total of 101 exemplar problems which are spread in 5 sections giving an exhaustive coverage of matrices. Instasolv has an amazing team of maths experts who give a lucid explanation of all the exemplar problems which is simple to understand. They will also thorough you with the know-how of the subject so that you can deal with the problems independently. These exemplar solutions can be referred to by you while taking their CBSE or any other competitive exams.
Important Topics for NCERT Maths Exemplar Solutions Class 12 Chapter 3
- Matrix and order of a matrix: Matrix is a rectangular array of entities which can be numbers, symbols or equations/expressions. They are arranged in rows and columns. The entities are arranged within brackets [ ] or (). The number of rows and columns in a matrix determines its order. So a matrix with rows and b columns is said to be of order “a x b”.
- Matrices types – Based on their order, elements and few other conditions, matrices can be categorized as below:
- Row matrix – A matrix with only 1 row but many columns:
- Column matrix – A matrix with only one column but many rows:
- Square matrix – A matrix where the number of rows and columns are equal is called a square matrix.
- Rectangular matrix – If the number of rows and columns are not equal then that makes a rectangular matrix.
- Diagonal matrix – A square matrix where all the non-diagonal numbers are 0 is a diagonal matrix.
Mij = 0, where i,j are row and column ordinal position and i ≠ j
- Scalar matrix – A diagonal matrix where all its diagonal elements are equal and non-zero is called a scalar matrix.
Mij = 0, where i ≠ j
Mij = c, where i = j, c is some non-zero constant
- Zero or null matrix – A matrix with all its elements as 0 is a zero/null matrix. It is denoted by O
[0 0 0 0]
- Identity/Unit matrix – A diagonal matrix where all its diagonal elements are equal to 1 is an identity matrix and is denoted by I.
Mij = 0, where i ≠ j
Mij = 1, where i = j
- Upper triangular matrix – A square matrix where all the elements above diagonal are non-zero and all below it are zero is an upper triangular matrix.
- Lower triangular matrix – A square matrix where all the elements below the diagonal are non-zero and all above it are zero is an upper triangular matrix.
- Equality of matrices – 2 matrices are said to be equal if they have the same order and their corresponding elements are equal. Below 2 matrices are equal:
[12 3 5 9] = [12 3 5 9]
- Matrix operations: One can do 3 basic mathematical operations on matrices of the same order, they are: addition, subtraction, and multiplication
- Addition – When you sum corresponding elements of 2 matrices M1 and M2 of order a x b, you get a matrix M3 of order a x b where its elements are the summation of elements of M1 and M2.
[1 3 5 4] + [12 -3 5 9] = [13 0 10 13]
- Subtraction – When you subtract corresponding elements of 2 matrices M1 and M2 of order a x b, you get a matrix M3 of order a x b where its elements are elements of M1 – elements of M2.
[1 3 5 4] – [12 -3 5 9] = [-11 6 0 -5]
- Multiplication = For multiplication, the number of columns of M1 should be equal to the number of rows of M2 and we obtain the new matrix by multiplying the first row of M1 with corresponding elements of the first column of M2 and then adding them up. If M1 is of order m x n, and M2 is of order n x p then the resultant matrix M3 will have the order m x p.
[1 3 5 4] * [12 -3 5 9] = [27 24 70 21]
- Transpose of a matrix = If one flips a matrix over its diagonal you get the transpose of that matrix. The new matrix has its rows which were columns of the original matrix.
Discussion of Exercises of NCERT Exemplar Class 12 Maths Solutions Chapter 3
- The first set of Exemplar problems for CBSE Class 12 Maths Chapter 1 is short answer types that touch the concepts around the order of a matrix and how to construct a matrix given a few conditions. It also has questions on the various mathematical operations performed on matrices. It has 48 questions.
- The second set is a long answer type with topics ranging from mathematical induction on matrices, the inverse of matrices, and elementary row transformations. It has 4 questions.
- The third set of questions is MCQ which is centred around types of matrices, the concept of permutations around matrix formation, mathematical operation on matrices, and order of a matrix. It has 15 questions.
- The fourth set of NCERT exemplar problems is filled in the blanks type which again touches all topics like types of matrices and operations on matrices. It has 14 questions.
- The fifth set is a true and false type with questions on equality of matrices, laws on operations on matrices, and order of matrices. It has 20 questions.
- The questions of NCERT Exemplar for class 12 are very important for students to prepare for their boards as well as competitive exams like IIT JEE and others. These questions enable students to employ their intellect and get thorough with all the concepts of a topic.
Why Use NCERT Maths Exemplar Solutions Class 12 Chapter 3 by Instasolv?
Instasolv has a highly qualified team of subject matter experts which helps students get a strong grip on maths. The NCERT Exemplar problems for Class 12 Maths Chapter 3 are solved in the simplest way with an emphasis on every detail which allows you to get a better grasp of any topic being discussed. It also helps them in handling the stressful CBSE board exams with better time management. To score well in the exam, you should only look up to NCERT Solutions and NCERT Exemplar Class 6 Science Solutions as they are self-sufficient and cover the entire syllabus of CBSE.