NCERT Solutions for Class 12 Maths Chapter 4 Determinants

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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:

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CBSE CLASS XII Related Questions

1.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

View Solution

2.
Let $ A $ be a matrix of order $ m \times n $ and $ B $ be a matrix such that $ A^T B $ and $ B A^T $ are defined. Then, the order of $ B $ is:

View Solution

3.
Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?

$f$ has a minimum value at $x = 0$
$f$ has no maximum value in $\mathbb{R}$
$f$ is continuous at $x = 0$
$f$ is differentiable at $x = 0$

View Solution

4.
The integrating factor of the differential equation $ \frac{dy}{dx} + y = \frac{1 + y}{x} $ is:

View Solution

5.
Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:

$x^3 + 3x^2 + \frac{2}{x^2} + 5x + 11$
$x^3 + 3x^2 + \frac{2}{x^2} + 5x - 11$
$x^3 + 3x^2 - \frac{2}{x^2} + 5x - 11$
$x^3 - 3x^2 - \frac{2}{x^2} + 5x - 11$

View Solution

6.
Let the polished side of the mirror be along the line \[ \frac{x}{1} = \frac{1 - y}{2} = \frac{2z - 4}{6}. \] A point $ P(1, 6, 3) $, some distance away from the mirror, has its image formed behind the mirror. Find the coordinates of the image point and the distance between the point $ P $ and its image.

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.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

2.
Let \( A \) be a matrix of order \( m \times n \) and \( B \) be a matrix such that \( A^T B \) and \( B A^T \) are defined. Then, the order of \( B \) is:

3.
Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?

4.
The integrating factor of the differential equation \( \frac{dy}{dx} + y = \frac{1 + y}{x} \) is:

5.
Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:

Similar Mathematics Concepts

Comments

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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. Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

2.Let \( A \) be a matrix of order \( m \times n \) and \( B \) be a matrix such that \( A^T B \) and \( B A^T \) are defined. Then, the order of \( B \) is:

3.Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?

4.The integrating factor of the differential equation \( \frac{dy}{dx} + y = \frac{1 + y}{x} \) is:

5.Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is:

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

2.
Let \( A \) be a matrix of order \( m \times n \) and \( B \) be a matrix such that \( A^T B \) and \( B A^T \) are defined. Then, the order of \( B \) is:

3.
Let $f(x) = |x|$, $x \in \mathbb{R}$. Then, which of the following statements is incorrect?

4.
The integrating factor of the differential equation \( \frac{dy}{dx} + y = \frac{1 + y}{x} \) is:

5.
Let $f'(x) = 3(x^2 + 2x) - \frac{4}{x^3} + 5$, $f(1) = 0$. Then, $f(x)$ is: