Class 12 CBSE Applied Maths Determinants Exercise 4.5

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.


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Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.6 Exercise 4.7 Exercise 4.8 Exercise 4.9 Case Study

Using Cramer's rule, solve the following (1 to 7) systems of linear equations :
Q1. (i) 3x +y=5 ,x+2y=3
(ii) 2x -y =17 , 3x + 5y = 6.

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Q2. (i) 2x -7y-13=0 , 5x + 6y-9 =0
(ii) 2/x + 3/y = 2, 5/x + 8/y = 31/6

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Q3. 3x + ay =4, 2x + ay = 2,a #0.

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Q4. (i) 5x-7y+z=11 , 6x - 8y -z = 15, 3x + 2y -6z = 7
(ii) x+y+z+1= 0, x+2y+3z+4=0, x+ 3y+4z+6=0.

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Q5. (i) 4x - 2y +9z +2=0 , ax+4y+z-5=0 ,x-3y+2z-8=0
(ii) x+y=2 , 2x-z=1 , 2y - 3z = 1

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Q6. (i) 2x-3y= 1, x+3z=11 , x+2y+z= 7
(ii)

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Q7. x + y + z = 1
ax + by +cz=k
a2x + b2y + c2z = k2 where a, b, c are all different.

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Q8. The sum of three numbers is 20. If we multiply the first number by 2 and add the second number to the result and subtract the third number, we get 23. By adding second and third numbers to three times the first number, we get 46. Represent the above problem algebraically and use Cramer’s rule to find the numbers from these equations.

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Q9. Which of the following equations are consistent? If consistent, solve them.

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Q10. Which of the following equations are consistent? If consistent, solve them.

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Q11. Which of the following systems has non-trivial solutions? If so, find these solutions.

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Q12. If the system of equations x - ky - z = 0, kx - y-z=0,x + y-z = O'has a non-zero solution, then find the possible values of k.

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Q13. Find the real value(s) of a for which the system of equations
x+ay=0,y+az=0,z+ax=0
has infinitely many solutions.

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Q14. If the equations x = cy + bz, y = az + cx, z = bx + ay are consistent, prove that
a2 + b2 + c2 + 2abc = 1.

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