Solve the following system of equations by matrix method:

5x + 7y + 2 = 0

4x + 6y + 3 = 0

Solve the following system of equations by matrix method:

5x + 2y = 3

3x + 2y = 5

Solve the following system of equations by matrix method:

3x + 4y = 5

x – y = – 3

Solve the following system of equations by matrix method:

3x + y = 19

3x – y = 23

Solve the following system of equations by matrix method:

3x + 7y = 4

x + 2y = – 1

Solve the following system of equations by matrix method:

3x + y = 7

5x + 3y = 12

Solve the following system of equations by matrix method:

x + y –z = 3

2x + 3y + z = 10

3x – y – 7z = 1

Solve the following system of equations by matrix method:

x + y + z = 3

2x – y + z = – 1

2x + y – 3z = – 9

Solve the following system of equations by matrix method:

6x – 12y + 25z = 4

4x + 15y – 20z = 3

2x + 18y + 15z = 10

Solve the following system of equations by matrix method:

3x + 4y + 7z = 14

2x – y + 3z = 4

X + 2y – 3z = 0

Solve the following system of equations by matrix method:

5x + 3y + z = 16

2x + y + 3z = 19

X + 2y + 4z = 25

Solve the following system of equations by matrix method:

3x + 4y + 2z = 8

2y – 3z = 3

x – 2y + 6z = – 2

Solve the following system of equations by matrix method:

2x + y + z = 2

x + 3y –z = 5

3x + y – 2z = 6

Solve the following system of equations by matrix method:

2x + 6y = 2

3x – z = – 8

2x – y + z = – 3

Solve the following system of equations by matrix method:

2y – z = 1

x – y + z = 2

2x – y = 0

Solve the following system of equations by matrix method:

8x + 4y + 3z = 18

2x + y + z = 5

X + 2y + z = 5

Solve the following system of equations by matrix method:

x + y + z = 6

x + 2z = 17

3x + y + z = 12

Solve the following system of equations by matrix method:

Solve the following system of equations by matrix method:

x – y + 2z = 7

3x + 4y – 5z = – 5

2x – y + 3z = 12

Show that each of the following systems of linear equations is consistent and also find their

6x + 4y = 2

9x + 6y = 3

Show that each of the following systems of linear equations is consistent and also find their

2x + 3y = 5

6x + 9y = 15

Show that each of the following systems of linear equations is consistent and also find their

Solutions :

5x + 3y + 7z = 4

3x + 26y + 2z = 9

7x + 2y + 10z = 5

Show that each of the following systems of linear equations is consistent and also find their

Solution:

x + y + z = 6

x + 2y + 3z = 14

x + 4y + 7z = 30

Show that each of the following systems of linear equations is consistent and also find their

Solution:

2x + 2y – 2z = 1

4x + 4y – z = 2

6x + 6y + 2z = 3

Show that each one of the following systems of linear equations is inconsistent

2x + 5y = 7

6x + 15y = 13

Show that each one of the following systems of linear equations is inconsistent

2x + 3y = 5

6x + 9y = 10

Show that each one of the following systems of linear equations is inconsistent

4x – 2y = 3

6x – 3y = 5

Show that each one of the following systems of linear equations is inconsistent

4x – 5y – 2z = 2

5x – 4y + 2z = – 2

2x + 2y + 8z = – 1

Show that each one of the following systems of linear equations is inconsistent

3x – y – 2z = 2

2y – z = – 1

3x – 5y = 3

Show that each one of the following systems of linear equations is inconsistent

x + y – 2z = 5

x – 2y + z = – 2

– 2x + y + z = 4

If and are two square matrices, find A B and hence solve the system of linear equations: X – y = 3, 2x + 3y + 4z = 17, y + 2z = 7.

If , find A ^{– 1} and hence solve the system of linear equations:2 x – 3 y + 5z = 11, 3x + 2y – 4z = – 5, x + y – 2z = – 3

Find A ^{– 1}, if . Hence, solve the following system of linear equations:

x + 2y + 5z = 10, x – y – z = – 2,

2x + 3y – z = – 11

Solve the following questions.

If , find A ^{– 1}. Using A ^{– 1}, solve the system of linear equations:

x – 2y = 10, 2x + y + 3z = 8, – 2y + z = 7.

Solve the following questions.

, find A ^{– 1} and hence solve the following system of equations:

3x – 4y + 2z = – 1, 2x + 3y + 5z = 7, x + z = 2.

Solve the following questions.

, find AB. Hence, solve the system of equations:

x – 2y = 10, 2x + y + 3z = 8 and – 2y + z = 7

Solve the following questions.

If , find A ^{– 1}. Using A ^{– 1}, solve the system of linear equations

x – 2y = 10, 2x – y – z = 8, – 2y + z = 7.

Solve the following questions.

Given , find BA and use this to solve the system of equations y + 2z = 7, x – y = 3, 2x + 3y + 4z = 17

The sum of three numbers is 2. If twice the second number is added to the sum of first and third, the sum is 1. By adding second and third number to five times the first number, we get 6. Find the three numbers by using matrices.

An amount of ₹10,000 is put into three investments at the rate of 10, 12 and 15% per annum. The combined incomes are ₹1310 and the combined income of first and second investment is ₹ 190 short of the income from the third. Find the investment in each using matrix method.

A company produces three products every day. Their production on a certain day is 45 tons. It is found that the production of the third product exceeds the production of a first product by 8 tons while the total production of a first and third product is twice the production of the second product. Determine the production level of each product using the matrix method.

The prices of three commodities P,Q and R and ₹ x,y and z per unit respectively. A purchases 4 units of R and sells 3 units of P and 5 units of Q. B purchases 3 units of Q and sells 2 units of P and 1 unit of R. C purchases 1 unit of Q. B purchases of Q and 6 units of R. In the process A, B and C earn ₹6000, ₹5000 and ₹13000 respectively. If selling the units is positive earning and buying the units is negative earnings, find the price per unit of three commodities by using the matrix method.

The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others (say z) for supervising the workers to keep the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. If the sum of the number of awardees for honesty and supervision is twice the number of awardees for helping others, using matrix method, find the number of awardees of each category. A part from these values, namely, honesty cooperation and supervision, suggest one more value which the management must include for awards.

A school wants to award its student for the values of Honesty, Regularity and Hard work with a total cash award of ₹6000. Three times the award money for Hard work added to that given for honesty amounts to ₹11000. The award money given for Honesty and Hard work together is double the one given for Regularity. Represent the above situation algebraically and find the award for each value, using the matrix method. Apart from these values, namely, Honesty, Regularity and Hard work, and suggest one more value which the school must include for awards.

Two institutions decided to award their employees for the three values resourcefulness, competence and determination in the from of prizes at the rate of₹x, ₹y and ₹z respectively per person. The first institutions decided to award respectively 4,3 and 2 employees with total prize money of ₹37000 and the second institution decided to award respectively 5,3 and 4 employees with total prize money of ₹47000. If all the three prizes per person together amount to ₹12000, then using matrix method find the value of x,y and z. What values are described in this equations?

Two factories decided to award their employees for three values of (a) adaptable to new techniques, (b) careful and alert in difficult situations and (c) keeping calm in tense situations, at the rate of ₹x, ₹y and ₹z per persons respectively. The first factory decided to honour respectively 2, 4 and 3 employees with total prize money of ₹29000. The second factory decided to honour respectively 5, 2 and 3 employees with the prize money of ₹30500. If the three prizes per person together cost ₹9500, then

i. represent the above situation by a matrix equation and form linear equations using matrix multiplication.

ii. Solve these equations using matrices.

iii. Which values are reflected in the questions?

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 total award money of ₹16,00. 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 the award.

Two schools P and Q want to award their selected students on the values of Discipline, Politeness and Punctuality. The school P wants to award ₹x each, ₹y each and ₹z each for the three respectively values to its 3, 2 and 1 students with a total award money of ₹1,000. School Q wants to spend ₹1,500 to award its 4,1 and 3 students on the respective values (by giving the same award money for three values as before.) If the total amount of awards for one prize on each value is ₹600, using matrices, find the award money for each value, Apart on each value is ₹600, using matrices, find the award money for each value, Apart from the above three values, suggest one more value for awards.

Two schools P and Q want to award their selected students on the values of Tolerance, Kindness and Leadership. The school P want to award ₹x each, ₹y each and ₹z each for the three respective values to 3,2 and 1 students respectively with total award money of ₹2,200. School Q wants to spend ₹3,100 to award its 4,1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each values is ₹1,200, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for the award

A total amount of ₹7000 is deposited in three different saving bank accounts with annual interest rates of 5%, 8% and respectively. The total annual interest from these three accounts is ₹550. Equal amounts have been deposited in the 5% and 8% savings accounts. Find the amount deposited in each of the three accounts, with the help of matrices.

A shopkeeper has 3 varities of pens ‘A’, ‘B’ and ‘C’. Meenu purchased 1 pen of each variety for a total of ₹21. Jeen purchased 4 pens of ‘A’ variety, 3 pens of ‘B’ variety and 2 pens of ‘C’ variety for ₹60. While Shikha purchased 6 pens of ‘A’ variety, 2 pens of ‘B’ variety and 3 pens of ‘C’ variety for ₹70. Using matrix method find the cost of each pen.

Solve the following systems of homogeneous linear equations by matrix method:

Solve the following systems of homogeneous linear equations by matrix method:

2x – y + 2z = 0

5x + 3y – z = 0

X + 5y – 5z = 0

Solve the following systems of homogeneous linear equations by matrix method:

3x – y + 2z = 0

4x + 3y + 3z = 0

5x + 7y + 4z = 0

Solve the following systems of homogeneous linear equations by matrix method:

x + y – 6z = 0

x – y + 2z = 0

– 3x + y + 2z = 0

Solve the following systems of homogeneous linear equations by matrix method:

x + y + z = 0

x – y – 5z = 0

x + 2y + 4z = 0

Solve the following systems of homogeneous linear equations by matrix method:

x + y – z = 0

x – 2y + z = 0

3x + 6y – 5z = 0

Solve the following systems of homogeneous linear equations by matrix method:

3x + y – 2z = 0

x + y + z = 0

x – 2y + z = 0

Solve the following systems of homogeneous linear equations by matrix method:

2x + 3y – z = 0

x – y – 2z = 0

3x + y + 3z = 0

Mark the correct alternative in the following:

The system of equation x + y + z = 2, 3x – y + 2z = 6 and 3x + y + z = –18 has

Mark the correct alternative in the following:

The number of solutions of the system of equations: x – 3y + 2z = 1, is

x + 4y – 3z = 5

Mark the correct alternative in the following:

Let and If AX = B, then X is equal to

Mark the correct alternative in the following:

The number of solutions of the system of equations:

2x + y – z = 7

x – 3y + 2z = 1, is

x + 4y – 3z = 5

Mark the correct alternative in the following:

The system of linear equations:

x + y + z = 2

2x + y – z = 3

3x + 2y + kz = 4 has a unique solution if

Mark the correct alternative in the following:

Consider the system of equations:

a₁x + b₁y + c₁z = 0

a₂x + b₂y + c₂z = 0

a₃x + b₃y + c₃z = 0

If then the system has

Mark the correct alternative in the following:

Let a, b, c be positive real numbers. The following system of equations in x, y and z

has

Mark the correct alternative in the following:

For the system of equations:

x + 2y + 3z = 1

2x + y + 3z = 2

5x + 5y + 9z = 4

Mark the correct alternative in the following:

The existence of the unique solution of the system of equations:

x + y + z = λ

5x – y + μz = 10

2x + 3y – z = 6 depends on

Mark the correct alternative in the following:

The system of equations:

x + y + z = 5

x + 2y + 3z = 9

x + 3y + λz = μ

has a unique solution, if

If find x, y and z.

If find x, y and z.

Solve for x and y.

If find x, y, z.

If and AX = B, then find n.