NCERT Solutions for Class 12 Maths Chapter 3 Matrices

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Class 12 Maths NCERT Solutions Chapter 3 Matrices is provided in the article below. A matrix is a rectangular grid in which numbers are arranged in rows and columns. There are many types of matrices and different operations that can be performed on them. Matrix is an important chapter in the Class 12 Maths Syllabus. The NCERT Solutions for Class 12 Mathematics Chapter 3 Matrices include concepts of types of matrices, operations on matrices, and symmetric and skew-symmetric matrices.

The chapter holds a weightage of about 10 marks in the CBSE Class 12 Examination along with the chapter Determinants. Generally, descriptive questions regarding solving for the values of x and y are asked from Matrices.

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Class 12 Maths NCERT Solutions Chapter 3 Matrices

NCERT Solutions

Important Topics in Class 12 Mathematics Chapter 3 Matrices

Matrices is an important chapter of Class 12 Mathematics. The chapter covers topics of types of matrices, operations on matrices, symmetric and skew symmetric matrices, transpose of a matrix, elementary operation on matrix and invertible matrices. The main topics of the chapter include:

A matrix is a function consisting of an ordered rectangular array of numbers. If a matrix has m rows with n columns, then it is known as the matrix of order m x n.

The various types of matrices are Column matrix, Row matrix, Square matrix, Diagonal matrix, Scalar matrix, Identity matrix, and Zero matrix

If A = [a_ij] be a m x n matrix, then the matrix that is obtained by interchanging the rows and columns of A is known as the transpose of A and is denoted by A′ or (A^T).

For example, matrix A = \([ \begin{matrix} 2 &1 & 3 \\ -4 & 0 & 5 \\ \end{matrix} ]\),then transpose of A, (A^T) = \([ \begin{matrix} 2 & -4 \\ 1 & 0 \\ 3 & 5 \end{matrix} ]\)

A square matrix A = [a_ij] is symmetric matrix if the transpose of A is equal to A, i.e. [a_ij] = [a_ji] for all possible values of i and j.

A square matrix A = [aij] is said to be a skew-symmetric matrix if A′ = – A, that is a_ji= – a_ij for all possible values of i and j.

Invertible Matrix – If a square matrix A of order m, and another square matrix B of the same order m, satisfies AB = BA = I, then B is the inverse matrix of A, and is denoted by A^-1.

NCERT Solutions For Class 12 Maths Chapter 3 Exercises

The detailed solutions for all the NCERT Solutions for Matrices under different exercises are as follows:

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CBSE CLASS XII Related Questions

1.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]
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2.
A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.
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3.
The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that
(i) target is hit.
(ii) at least one shot misses the target.
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4.
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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5.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]
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6.
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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