NCERT Solutions for Class 12 Maths Chapter 4 Determinants

Education Journalist | Study Abroad Lead

NCERT Solutions for Class 12 Maths Chapter 4 Determinants covers important concepts of Determinants of a matrix and inverse of a matrix. A determinant of the matrix is a scalar value that is calculated using a square matrix. To every square matrix, we can associate a number that is real or complex. The determinant is denoted by det A or |A|. The NCERT Solutions of Chapter 4 Determinants deals with properties of determinants, area of a triangle, minors and cofactors, and applications of matrices and determinants.

The unit algebra comprising Chapter 3 Matrices and Chapter 4 Determinants has a weightage of 10 marks in the final CBSE Board examination. The questions asked from the chapter generally include adjoint and inverse matrices, finding the determinants of a given matrix, and solving a system of linear equations in two or three variables

Download PDF: NCERT Solutions for Chapter 4 Determinants

NCERT Solutions for Class 12 Mathematics Chapter 4 Determinants

Important Topics in Class 12 Mathematics Chapter 4 Determinants

Each square matrix of the order n can associate a number known as determinants of the square matrix A. It can be of orders one, two, and three.

Determinant of order one: Consider a matrix A = [a], the determinant of this matrix is equal to a. Determinant of order two: If the order of the matrix is 2, and the given matrix A is- \([ \begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22}\\ \end{matrix} ]\) Determinant of A, \|A\| = \(\| \begin{matrix} a_{11} & a_{12} \\ a_{21} & a_{22}\\ \end{matrix} \|\), = a₁₁.a₂₂- a₂₁.a₁₂ Determinant of order three: If the order of the matrix is 2, and the given matrix A is- \([ \begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33}\\ \end{matrix} ]\) Determinant of A, \|A\| = a₁₁ a₂₂ a₃₃ – a₁₁ a₂₃ a₃₂ – a₁₂ a₂₁ a₃₃ + a₁₂ a₂₃ a₃₁ + a₁₃ a₂₁ a₃₂ – a₁₃ a₃₁ a₂₂

The area of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by – A = ½ [x₁(y₂–y₃) + x₂(y₃–y₁) + x₃(y₁–y₂)].

We can find the area of a triangle using determinants by \(\begin{array}{l}\Delta = \frac{1}{2}\begin{vmatrix} x_{1} & y_{1} & 1\\ x_{2} & y_{2} & 1\\ x_{3} & y_{3} & 1 \end{vmatrix}\end{array}\)

Minors and Cofactors: Suppose \(\begin{array}{l}\Delta = \begin{vmatrix} a & b & c\\ d & e & f\\ g & h & i \end{vmatrix}\end{array}\)

Minor = \(\begin{array}{l}M_{f}=\begin{vmatrix} a & b\\ g & h \end{vmatrix}\end{array}\), M_f = a.h – b.g Cofactor of an element a_ij in determinant is defined as A_ij= (-1)^i+jM_ij

NCERT Solutions For Class 12 Maths Chapter 4 Exercises:

The detailed solutions for all the NCERT Solutions for Chapter 4 Determinants under different exercises are as follows:

Also Read:

Related Articles
Minors and Cofactors	Non Singular Matrix	Consistent and Inconsistent system of equations
Determinant Formula	Elementary Matrix Operations	Applications of Determinants and Matrices
Difference between rows and columns	Jacobian Method	Inverse Laplace Transform

Check-Out:

PCMB Study Guides
NCERT Solutions for Class 12 Physics	Class 12 Physics Notes	Formulas in Physics
Topics for Comparison in Physics	Choice-based questions in physics	Topics in relation to physics
Physics Study Notes	Class 12 Physics Book PDF	Class 12 Physics Practicals
Important Derivations in Physics	SI units in Physics	Important Physics Constants and Units
Class 12 Physics Syllabus	Mendeleev's Periodic Table	NCERT Solutions for Class 12 Biology
NCERT Solutions for Class 12 English	NCERT Solutions for Class 11 Chemistry	Class 12 Chemistry Practicals
Class 12 Chemistry Notes	Important Chemical Reactions	Class 12 Maths Notes
Class 12 PCMB Notes	NCERT Class 12 Biology Book	NCERT Class 12 Maths Book
NCERT Class 12 Textbooks	NCERT Solutions for Class 11 Maths	NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 12 Maths	NCERT Solutions for Class 11 Biology	NCERT Solutions for Class 11 English
NCERT Class 11 Chemistry Book	NCERT Class 11 Physics Book	NCERT Class 11 Biology Book
Class 11 Notes	Important Maths Formulas	Important Chemistry Formulas
Class 11 PCMB Syllabus	Chemistry Study Notes	Biology Study Notes
Periodic Table in Chemistry	Important Chemical Reactions	Comparison topics in Chemistry
Comparison Topics in Maths	Biology MCQs	Important Named Reactions
Maths MCQs	Comparison Topics in Biology	Chemistry MCQs

CBSE CLASS XII Related Questions

1.
The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

\( e^{-3} \)
\( -1 \)
\( 1 \)
\( -e^3 \)

View Solution

2.
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:

3.
For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

local maximum value is 2
local minimum value is \( -2 \)
local maximum value is \( -2 \)
local minimum value \( < \) local maximum value

View Solution

4.
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.

View Solution

5.
Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]

View Solution

6.
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.

View Solution

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

NCERT Solutions for Class 12 Mathematics Chapter 4 Determinants

Important Topics in Class 12 Mathematics Chapter 4 Determinants

NCERT Solutions For Class 12 Maths Chapter 4 Exercises:

CBSE CLASS XII Related Questions

1.
The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

3.
For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

4.
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 \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

5.
Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]

6.
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): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

NCERT Solutions for Class 12 Mathematics Chapter 4 Determinants

Important Topics in Class 12 Mathematics Chapter 4 Determinants

NCERT Solutions For Class 12 Maths Chapter 4 Exercises:

CBSE CLASS XII Related Questions

1. The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

3. For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

4.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 \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

5.Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]

6.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): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:

3.
For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

4.
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 \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).

5.
Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]

6.
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): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]