NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.6

Get Free NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.6 PDF in Hindi and English Medium. Sets Class 12 Maths NCERT Solutions are extremely helpful while doing your homework. Determinants Exercise 4.6 Class 12 Maths NCERT Solutions were prepared by Experienced LearnCBSE.in Teachers. Detailed answers of all the questions in Chapter 4 Class 12 Determinants Ex 4.6 provided in NCERT Textbook.

Free download NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.6 PDF in Hindi Medium as well as in English Medium for CBSE, Uttarakhand, Bihar, MP Board, Gujarat Board, BIE, Intermediate and UP Board students, who are using NCERT Books based on updated CBSE Syllabus for the session 2019-20.

The topics and sub-topics included in the Determinants chapter are the following:

Section Name	Topic Name
4	Determinants
4.1	Introduction
4.2	Determinant
4.3	Properties of Determinants
4.4	Area of a Triangle
4.5	Adjoint and Inverse of a Matrix
4.6	Applications of Determinants and Matrices
4.7	Summary

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.6

Examine the consistency of the system of equations in Questions 1 to 6:

Ex 4.6 Class 12 Maths Question 1.
x + 2y = 2
2x + 3y = 3
Solution:
x + 2y = 2,
2x + 3y = 3
=> Image may be NSFW.
Clik here to view. $\begin{bmatrix} 1 & 2 \\ 2 & 3 \end{bmatrix}\left[ \begin{matrix} x \\ y \end{matrix} \right] =\left[ \begin{matrix} 2 \\ 3 \end{matrix} \right]$
=> AX = B
Now |A| = Image may be NSFW.
Clik here to view. $\begin{vmatrix} 1 & 2 \\ 2 & 3 \end{vmatrix}$
= 3 – 4
= – 1 ≠ 0.
Hence, equations are consistent.

Ex 4.6 Class 12 Maths Question 2.
2x – y = 5
x + y = 4
Solution:
2x – y = 5,
x + y = 4
=> Image may be NSFW.
Clik here to view. $\begin{bmatrix} 2 & -1 \\ 1 & 1 \end{bmatrix}\left[ \begin{matrix} x \\ y \end{matrix} \right] =\left[ \begin{matrix} 5 \\ 4 \end{matrix} \right]$
=> AX = B
Now |A| = Image may be NSFW.
Clik here to view. $\begin{vmatrix} 2 & -1 \\ 1 & 1 \end{vmatrix}$
= 2 + 1
= 3 ≠ 0.
Hence, equations are consistent.

Ex 4.6 Class 12 Maths Question 3.
x + 3y = 5,
2x + 6y = 8
Solution:
x + 3y = 5,
2x + 6y = 8
=> Image may be NSFW.
Clik here to view. $\begin{bmatrix} 1 & 3 \\ 2 & 6 \end{bmatrix}\left[ \begin{matrix} x \\ y \end{matrix} \right] =\left[ \begin{matrix} 5 \\ 8 \end{matrix} \right]$
=> AX = B
Now |A| = Image may be NSFW.
Clik here to view. $\begin{vmatrix} 1 & 3 \\ 2 & 6 \end{vmatrix}$
= 6 – 6
= 0.
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 3
Hence, equations are consistent with no solution

Ex 4.6 Class 12 Maths Question 4.
x + y + z = 1
2x + 3y + 2z = 2
ax + ay + 2az = 4
Solution:
x + y + z = 1
2x + 3y + 2z = 2
x + y + z = Image may be NSFW.
Clik here to view. $\\ \frac { 4 }{ a }$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 4

Ex 4.6 Class 12 Maths Question 5.
3x – y – 2z = 2
2y – z = – 1
3x – 5y = 3
Solution:
Image may be NSFW.
Clik here to view. $\left[ \begin{matrix} 3 & -1 & -2 \\ 0 & 2 & -1 \\ 3 & -5 & 0 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 2 \\ -1 \\ 3 \end{matrix} \right]$
=> AX = B
Image may be NSFW.
Clik here to view. byjus class 12 maths Chapter 4 Determinants 5
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 5.1

Ex 4.6 Class 12 Maths Question 6.
5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = -1
Solution:
Given
5x – y + 4z = 5
2x + 3y + 5z = 2
5x – 2y + 6z = -1
Image may be NSFW.
Clik here to view. $\left[ \begin{matrix} 5 & -1 & 4 \\ 2 & 3 & 5 \\ 5 & -2 & 6 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 5 \\ 2 \\ -1 \end{matrix} \right]$
Image may be NSFW.
Clik here to view. $AX=B|A|=\left[ \begin{matrix} 5 & -1 & 4 \\ 2 & 3 & 5 \\ 5 & -2 & 6 \end{matrix} \right]$
= 5(18 + 10)+1(12 – 25)+4(-4-15)
= 140-13-76
= 51 ≠ 0
Hence equations are consistent with a unique
solution.

Solve system of linear equations using matrix method in Questions 7 to 14:

Ex 4.6 Class 12 Maths Question 7.
5x + 2y = 4
7x + 3y = 5
Solution:
The given system of equations can be written as
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 7
Image may be NSFW.
Clik here to view. byjus class 12 maths Chapter 4 Determinants 7.1

Ex 4.6 Class 12 Maths Question 8.
2x – y = – 2
3x + 3y = 3
Solution:
The given system of equations can be written
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 8

Ex 4.6 Class 12 Maths Question 9.
4x – 3y = 3
3x – 5y = 7
Solution:
The given system of equations can be written as
Image may be NSFW.
Clik here to view. $\begin{bmatrix} 4 & -3 \\ 3 & -5 \end{bmatrix}\left[ \begin{matrix} x \\ y \end{matrix} \right] =\left[ \begin{matrix} 3 \\ 7 \end{matrix} \right] i.e,,AX=B$
where Image may be NSFW.
Clik here to view. $A=\begin{bmatrix} 4 & -3 \\ 3 & -5 \end{bmatrix}$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 9

Ex 4.6 Class 12 Maths Question 10.
5x + 2y = 3
3x + 2y = 5
Solution:
The given system of equations can be written as
Image may be NSFW.
Clik here to view. $\begin{bmatrix} 5 & 2 \\ 3 & 2 \end{bmatrix}\left[ \begin{matrix} x \\ y \end{matrix} \right] =\left[ \begin{matrix} 3 \\ 5 \end{matrix} \right] i.e,,AX=B$
where Image may be NSFW.
Clik here to view. $A=\begin{bmatrix} 5 & 2 \\ 3 & 2 \end{bmatrix}$
Image may be NSFW.
Clik here to view. byjus class 12 maths Chapter 4 Determinants 10

Ex 4.6 Class 12 Maths Question 11.
2x + y + z = 1,
x – 2y – z = 3/2
3y – 5z = 9
Solution:
The given system of equations are
2x + y + z = 1,
x – 2y – z = 3/2,
3y – 5z = 9
We know AX = B => X = A^-1B
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 11

Ex 4.6 Class 12 Maths Question 12.
x – y + z = 4
2x + y – 3z = 0
x + y + z = 2.
Solution:
The given system of equations can be written
Image may be NSFW.
Clik here to view. $\left[ \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 4 \\ 0 \\ 2 \end{matrix} \right] i.e,,AX=B$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 12
Image may be NSFW.
Clik here to view.

Ex 4.6 Class 12 Maths Question 13.
2x + 3y + 3z = 5
x – 2y + z = – 4
3x – y – 2z = 3
Solution:
The given system of equations can be written as:
Image may be NSFW.
Clik here to view. $\left[ \begin{matrix} 2 & 3 & 3 \\ 1 & -2 & 1 \\ 3 & -1 & -2 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 5 \\ -4 \\ 3 \end{matrix} \right] i.e,,AX=B$
Image may be NSFW.
Clik here to view. byjus class 12 maths Chapter 4 Determinants 13
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 13.1

Ex 4.6 Class 12 Maths Question 14.
x – y + 2z = 7
3x + 4y – 5z = – 5
2x – y + 3z = 12.
Solution:
The given system of equations can be written
Image may be NSFW.
Clik here to view. $\left[ \begin{matrix} 1 & -1 & 2 \\ 3 & 4 & -5 \\ 2 & -1 & 3 \end{matrix} \right] \left[ \begin{matrix} x \\ y \\ z \end{matrix} \right] =\left[ \begin{matrix} 7 \\ -5 \\ 12 \end{matrix} \right] i.e,,AX=B$
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 14
Image may be NSFW.
Clik here to view.

Ex 4.6 Class 12 Maths Question 15.
If A = Image may be NSFW.
Clik here to view. $\left[ \begin{matrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{matrix} \right]$ Find A^-1. Using A^-1. Solve the following system of linear equations 2x – 3y + 5z = 11,3x + 2y – 4z = – 5, x + y – 2z = – 3
Solution:
We have AX = B
where Image may be NSFW.
Clik here to view. $A=\left[ \begin{matrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{matrix} \right] ,X=\left[ \begin{matrix} x \\ y \\ z \end{matrix} \right]$
Image may be NSFW.
Clik here to view. byjus class 12 maths Chapter 4 Determinants 15

Ex 4.6 Class 12 Maths Question 16.
The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs. 69. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs. 90. The cost of 6 kg onion, 2 kg wheat and 3 kg rice is Rs. 70. Find the cost of each item per kg by matrix method
Solution:
Let cost of 1 kg onion = Rs x
and cost of 1 kg wheat = Rs y
and cost of 1 kg rice = Rs z
4x+3y+2z=60
2x+4y+6z=90
6x+2y+3z=70
Image may be NSFW.
Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Determinants 16

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Hindi Medium Ex 4.6

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Clik here to view. NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.6 Determinants
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Clik here to view. Class 12 Maths Chapter 4 Exercise 4.6 solutions for UP Board
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Clik here to view. NCERT Solutions 12 Maths Exercise 4.6 Hindi me
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Clik here to view. Class 12 Maths Chapter 4 Exercise 4.6 solutions Hindi me
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