NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.4

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Class 12 Maths NCERT Solutions Chapter 3 Matrices Exercise 3.4 is provided in this article. Chapter 3 Exercise 3.4 deals with problems related to the concepts of elementary operation of a Matrix, invertible matrices, and the inverse of a matrix by elementary operations.

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Check out other exercise solutions of Class 12 Maths Chapter 3 Matrices

Class 12 Chapter 3 Matrices Topics:
Transpose of a Matrix	Scalar Matrix Formula	Column Matrix
Matrix Multiplication	Orthogonal Matrix	Singular Matrix
Inverse Matrix Formula	Proof of the uniqueness of inverse, if it exists	Upper Triangular Matrix

Also check:

CBSE Class 12 Mathematics Study Guides:
Algebra	Arithmetic	Calculus
Mensuration	Trigonometry	Geometry
Permutation and Combination	Math Study Notes	Math MCQs
NCERT Solutions for Class 12 Maths	Math Formula	Difference between in Math

CBSE CLASS XII Related Questions

1.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).
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2.
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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3.
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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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.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.
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6.
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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