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.
If $ \mathbf{a} $ and $ \mathbf{b} $ are position vectors of two points $ P $ and $ Q $ respectively, then find the position vector of a point $ R $ in $ QP $ produced such that \[ QR = \frac{3}{2} QP. \]

View Solution

2.
Determine those values of $x$ for which $f(x) = \frac{2}{x} - 5$, $x \ne 0$ is increasing or decreasing.

View Solution

3.
Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

$[5, 10]$
$[-2, 5]$
$[2, 1]$
$[-10, 5]$

View Solution

4.
Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the $ x $-axis, and the ordinates $ x = -2 $ and $ x = 2 $.

View Solution

5.
The area of the shaded region (figure) represented by the curves $ y = x^2 $, $ 0 \leq x \leq 2 $, and the y-axis is given by:

$ \int_0^2 x^2 \, dx $
$ \int_0^2 \sqrt{y} \, dy $
$ \int_0^4 x^2 \, dx $
$ \int_0^4 \sqrt{y} \, dy $

View Solution

6.
$ \int \frac{e^{10 \log x} - e^{8 \log x}}{e^{6 \log x} - e^{5 \log x}} \, dx$ is equal to :

$x + C$
$\frac{x^2}{2} + C$
$\frac{x^4}{4} + C$
$\frac{x^3}{3} + C$

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.
If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]

2.
Determine those values of $x$ for which $f(x) = \frac{2}{x} - 5$, $x \ne 0$ is increasing or decreasing.

3.
Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

4.
Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the \( x \)-axis, and the ordinates \( x = -2 \) and \( x = 2 \).

5.
The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:

6.
$ \int \frac{e^{10 \log x} - e^{8 \log x}}{e^{6 \log x} - e^{5 \log x}} \, dx$ is equal to :

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.If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]

2.Determine those values of $x$ for which $f(x) = \frac{2}{x} - 5$, $x \ne 0$ is increasing or decreasing.

3.Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

4.Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the \( x \)-axis, and the ordinates \( x = -2 \) and \( x = 2 \).

5.The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:

6.$ \int \frac{e^{10 \log x} - e^{8 \log x}}{e^{6 \log x} - e^{5 \log x}} \, dx$ is equal to :

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]

2.
Determine those values of $x$ for which $f(x) = \frac{2}{x} - 5$, $x \ne 0$ is increasing or decreasing.

3.
Let $\mathbf{| \mathbf{a} |} = 5$ and $-2 \leq z \leq 1$. Then, the range of $|\mathbf{a}|$ is:

4.
Using integration, find the area of the region bounded by the line \[ y = 5x + 2, \] the \( x \)-axis, and the ordinates \( x = -2 \) and \( x = 2 \).

5.
The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:

6.
$ \int \frac{e^{10 \log x} - e^{8 \log x}}{e^{6 \log x} - e^{5 \log x}} \, dx$ is equal to :