Class 12 ISC Maths Chapter Determinants Exercise 4.5
Explore our extensive collection of questions on the topic of "Determinants," designed to help you understand and apply this fundamental concept in linear algebra. Our question bank covers key topics such as properties of determinants, cofactor expansion, minors, applications in solving systems of linear equations, and finding the inverse of matrices. These practice questions are perfect for students aiming to build a strong foundation in determinants and excel in exams. Whether you're revising concepts or looking to enhance your problem-solving skills, our comprehensive collection provides the ideal resource for mastering "Determinants."
class 12 Determinants exercise4-1
Determinants
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Q1
Use matrix method to solve the following system of equations :
Q2
Using matrix method, determine whether the following system of equation is consistent or inconsistent
Q4
Using matrix method, solve the following system of equations:
Q6
The sum of three numbers is 6. If we multiply third number by 3 and add second to it we get 11. By adding first and third numbers, we get double of the second number. Represent it algebraically and find the numbers using matrix method.
Q7(i)
Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award ₹x each, ₹y each and ₹z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹1,600. School B wants to spend ₹2,300 to award its 4,1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is ₹900, using matrices, find the award money for each value.
Apart from these three values, suggest one more value which should be considered for award
Q7(ii)
10 students were selected from a school on the basis of values for giving awards and were divided into three groups.The first group comprises hard workers, the second group has honest and law abiding students and the third group contains vigilant and obedient students. Double the number of students of the first group added to the number in the second group gives 13, while the combined strength of first and second group is four times that of the third group. Using matrix method, find the number of students in each group. Apart from the values, hard work, honesty and respect for law, vigilance and obedience, suggest one more value, which in your opinion,the school should consider for awards
Q8
If A=
1 2 -3 2 3 2 3 -3 -4
,find A-1. Using A-1, solve the system of linear equations:
x+ 2y-3z = - 4, 2x + 3y + 2z = 2, 3x - 3y-4z = 11.
| 1 | 2 | -3 |
| 2 | 3 | 2 |
| 3 | -3 | -4 |
Q9
If A=
2 -3 5 3 2 -4 1 1 -2
,find A-1. Using A-1, solve the system of linear equations:
2x-3y+5z = 11, 3x + 2y -4z = -5, x+y-2z =-3.
| 2 | -3 | 5 |
| 3 | 2 | -4 |
| 1 | 1 | -2 |
Q10
If A=
3 5 -2 3
,find A-1. Using A-1,
solve the system of linear equations:
3x-2y=7 , 5x+3y=1
| 3 | 5 |
| -2 | 3 |
Q11
If A=
1 -1 1 2 1 -3 1 1 1
,find A-1. Using A-1
, solve the system of linear equations:
x+ 2y+z = 4, -x +y +z = 0, x -3y+z = 2.
| 1 | -1 | 1 |
| 2 | 1 | -3 |
| 1 | 1 | 1 |
Q12
Given two matrices A and B where
A= 1 -2 3 1 4 1 1 -3 2
and B= 11 -5 -14 -1 -1 2 -7 1 6
, find AB and use this result to solve the following system of equations:
x- 2y + 3z = 6, x + 4y + z = 12, x - 3y + 2z = 1.
| 1 | -2 | 3 |
| 1 | 4 | 1 |
| 1 | -3 | 2 |
| 11 | -5 | -14 |
| -1 | -1 | 2 |
| -7 | 1 | 6 |
Q13
Using matrices, solve the following systems of homogeneous equations:
Q14
Using matrices, solve the following systems of homogeneous equations:
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