SECTION A(ONE MARK) If A is a square matrix of order 3×3 such that .Then find the value of . that x= -9 is the root of =0, what are the other two roots? SECTION B(TWO MARKS) Solve the equation 4. What is the of? If is a square matrix of order 3 such that , write the value of . 5. SECTION C (FOUR MARKS) 6.Show that If a2+ b2+ c2 =0 and = k a2 b2c2, then what is the value of k. 7. │ 8. A school wants to award its students for the values of honesty regularity and hard work with a total cash award of Rs 9000.Three times the award moneyfor hard work added to thatgiven for honesty amounts to Rs 16500. The award moneygiven for honesty and hard work together is double the onegiven for regularity. Represent the above situation algebraically and find the award money for each values. Suggest one more value which the school must include for awards. 9. If x,y, z are all different and 0, prove that p2(x + y + z) = │ │= 3xyz. 10. If a+ b +c = 0, solve for x: = 0. │ 11. Using properties of determinants, prove that = (. SECTION D (SIX MARKS) 12. Given that A = and B = , find AB and use it to solve te system of equation: x y +z = 4, x – 2y- 2z = 9, 2x + y + 3z =1. – 13. If a, b, c are all different and 0, then find the values of x. │ │= shopkeepers A, B, C are using polythene, handmade bags (prepared by prisoners), and newspaper’s envelope as carry bags. it is found that the shopkeepers A, B, C are using (20,30,40) , (30,40,20,),(40,20,30) polythene , handmade bags and newspapers envelopes respectively. The shopkeepers A, B, C spent Rs.250, Rs.220 & Rs.200 on these carry bags
SECTION A(ONE MARK) If A is a square matrix of order 3×3 such that .Then find the value of . that x= -9 is the root of =0, what are the other two roots? SECTION B(TWO MARKS) Solve the equation 4. What is the of? 5. If is a square matrix of order 3 such that , write the value of . SECTION C (FOUR MARKS) 6.Show that 7. If a2+ b2+ c2 =0 and │ = k a2 b2c2, then what is the value of k. 8. A school wants to award its students for the values of honesty regularity and hard work with a total cash award of Rs 9000.Three times the award moneyfor hard work added to thatgiven for honesty amounts to Rs 16500. The award moneygiven for honesty and hard work together is double the onegiven for regularity. Represent the above situation algebraically and find the award money for each values. Suggest one more value which the school must include for awards. 9. If x,y, z are all different and │ │= 0, prove that p2(x + y + z) = 3xyz. 10. If a+ b +c = 0, solve for x: │ = 0. 11. Using properties of determinants, prove that = (. SECTION D (SIX MARKS) 12. Given that A = and B = , find AB and use it to solve te system of equation: x – y +z = 4, x – 2y- 2z = 9, 2x + y + 3z =1. 13. If a, b, c are all different and │ │= 0, then find the values of x. shopkeepers A, B, C are using polythene, handmade bags (prepared by prisoners), and newspaper’s envelope as carry bags. it is found that the shopkeepers A, B, C are using (20,30,40) , (30,40,20,),(40,20,30) polythene , handmade bags and newspapers envelopes respectively. The shopkeepers A, B, C spent Rs.250, Rs.220 & Rs.200 on these carry bags