NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.2

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NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.2 is given in this article. Chapter 3 Exercise 3.2 includes questions related to operations on matrices, multiplication of a matrix by a scalar, and addition of matrices. The questions also cover the concepts of properties of scalar multiplication and the addition of matrices.

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Class 12 Chapter 3 Matrices Topics:

Types of Matrices	Transpose of a Matrix	Symmetric and Skew-symmetric matrices
Invertible Matrices	Scalar Matrix Formula	Identity Matrix
Column Matrix	Singular Matrix	Symmetric Matrix
Inverse Matrix Formula	Proof of the uniqueness of inverse, if it exists	Upper Triangular Matrix

CBSE Class 12 Mathematics Study Guides:

Algebra	Arithmetic	Difference between in Math
Geometry	NCERT Solutions for Class 12 Maths	Math Formula
Math MCQs	Calculus	Math Study Notes

CBSE CLASS XII Related Questions

1.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]
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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 one such track is given as

(i) Find \(f'(x)\) for \(0<x>3\).
(ii) Find \(f'(4)\).
(iii)(a) Test for continuity of \(f(x)\) at \(x=3\).
OR
(iii)(b) Test for differentiability of \(f(x)\) at \(x=3\).
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3.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).
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4.
If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]
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5.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]
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6.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following:

(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).
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