NCERT Solutions for Class 12 Maths Chapter 3 Matrices

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Class 12 Maths NCERT Solutions Chapter 3 Matrices is provided in the article below. A matrix is a rectangular grid in which numbers are arranged in rows and columns. There are many types of matrices and different operations that can be performed on them. Matrix is an important chapter in the Class 12 Maths Syllabus. The NCERT Solutions for Class 12 Mathematics Chapter 3 Matrices include concepts of types of matrices, operations on matrices, and symmetric and skew-symmetric matrices.

The chapter holds a weightage of about 10 marks in the CBSE Class 12 Examination along with the chapter Determinants. Generally, descriptive questions regarding solving for the values of x and y are asked from Matrices.

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Class 12 Maths NCERT Solutions Chapter 3 Matrices

NCERT Solutions

Important Topics in Class 12 Mathematics Chapter 3 Matrices

Matrices is an important chapter of Class 12 Mathematics. The chapter covers topics of types of matrices, operations on matrices, symmetric and skew symmetric matrices, transpose of a matrix, elementary operation on matrix and invertible matrices. The main topics of the chapter include:

A matrix is a function consisting of an ordered rectangular array of numbers. If a matrix has m rows with n columns, then it is known as the matrix of order m x n.

The various types of matrices are Column matrix, Row matrix, Square matrix, Diagonal matrix, Scalar matrix, Identity matrix, and Zero matrix

If A = [a_ij] be a m x n matrix, then the matrix that is obtained by interchanging the rows and columns of A is known as the transpose of A and is denoted by A′ or (A^T).

For example, matrix A = \([ \begin{matrix} 2 &1 & 3 \\ -4 & 0 & 5 \\ \end{matrix} ]\),then transpose of A, (A^T) = \([ \begin{matrix} 2 & -4 \\ 1 & 0 \\ 3 & 5 \end{matrix} ]\)

A square matrix A = [a_ij] is symmetric matrix if the transpose of A is equal to A, i.e. [a_ij] = [a_ji] for all possible values of i and j.

A square matrix A = [aij] is said to be a skew-symmetric matrix if A′ = – A, that is a_ji= – a_ij for all possible values of i and j.

Invertible Matrix – If a square matrix A of order m, and another square matrix B of the same order m, satisfies AB = BA = I, then B is the inverse matrix of A, and is denoted by A^-1.

NCERT Solutions For Class 12 Maths Chapter 3 Exercises

The detailed solutions for all the NCERT Solutions for Matrices under different exercises are as follows:

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CBSE CLASS XII Related Questions

1.
Find: \[ \int \frac{x^2}{(x^2+9)(x^2+16)}\,dx \]
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2.
Check whether \[ f:\mathbb{R}-\{3\}\rightarrow\mathbb{R} \] defined as \[ f(x)=\frac{x-2}{x-3} \] is onto or not.
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3.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).
- Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
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4.
Sports car racing is a form of motorsport which uses sports car prototypes.The competition is held on special tracks designed in various shapes.
The equation of a sports car racing track is given as: \[ f(x)= \begin{cases} x^4-4x^2+4, & 0\leq x<3,\\ x^2+40, & x\geq 3 \end{cases} \] Based on this information:
5.
For two vectors \(\vec{a}\) and \(\vec{b}\):

Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]
- Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
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6.
Check whether the function \[ f(x)= \begin{cases} \dfrac{|x-3|}{2(x-3)}, & x<3,\\[6pt] \dfrac{x-6}{6}, & x\geq 3 \end{cases} \] is continuous at \(x=3\) or not.
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