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

x + 2y = 9;

2x + 4y = 7.

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

2x + 3y = 5;

6x + 9y = 10.

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

4x – 2y = 3;

6x – 3y = 5.

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

6x + 4y = 5;

9x + 6y = 8.

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

x + y – 2z = 5;

x – 2y + z = - 2;

- 2x + y + z = 4.

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

2x – y + 3z = 1;

3x – 2y + 5z = - 4;

5x – 4y + 9z = 14.

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

x + 2y + 4z = 12;

y + 2z = - 1;

3x + 2y + 4z = 4.

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

3x – y – 2z = 2;

2y – z = - 1;

3x – 5y = 3.

Solve each of the following systems of equations using matrix method.

5x + 2y = 4;

7x + 3y = 5.

Solve each of the following systems of equations using matrix method.

3x + 4y – 5 = 0;

x - y + 3 = 0.

Solve each of the following systems of equations using matrix method.

x + 2y = 1;

3x + y = 4.

Solve each of the following systems of equations using matrix method.

5x + 7y + 2 = 0;

4x + 6y + 3 = 0.

Solve each of the following systems of equations using matrix method.

2x - 3y + 1 = 0;

x + 4y + 3 = 0.

Solve each of the following systems of equations using matrix method.

4x - 3y = 3;

3x - 5y = 7.

Solve each of the following systems of equations using matrix method.

2x + 8y + 5z = 5;

x + y + z = - 2;

x + 2y - z = 2.

Solve each of the following systems of equations using matrix method.

x – y + z = 1;

2x + y – z = 2;

X – 2y – z = 4.

Solve each of the following systems of equations using matrix method.

3X + 4y + 7z = 4;

2x – y + 3z = - 3;

x + 2y – 3z = 8.

Solve each of the following systems of equations using matrix method.

x + 2y + z = 7;

x + 3z = 11;

2x – 3y = 1.

Solve each of the following systems of equations using matrix method.

2x - 3y + 5z = 16;

3x + 2y – 4z = - 4

x + y – 2z = - 3.

Solve each of the following systems of equations using matrix method.

x + y + z = 4;

2x – y + z = - 1;

2x + y – 3z = - 9.

Solve each of the following systems of equations using matrix method.

2x - 3y + 5z = 11;

3x + 2y - 4z = - 5;

x + y – 2z = - 3.

Solve each of the following systems of equations using matrix method.

x + y + z = 1;

x – 2y + 3z = 2;

5x – 3y + z = 3.

Solve each of the following systems of equations using matrix method.

x + y + z = 6;

x + 2z = 7;

3x + y + z = 12.

Solve each of the following systems of equations using matrix method.

2x + 3y + 3z = 5;

x – 2y + z = - 4;

3x – y – 2z = 3.

Solve each of the following systems of equations using matrix method.

4x - 5y – 11z = 12;

X – 3y + z = 1;

2x + 3y – 7z = 2.

Solve each of the following systems of equations using matrix method.

x – y + 2z = 7;

3x + 4y – 5z = - 5:

2x – y + 3z = 12.

Solve each of the following systems of equations using matrix method.

6X - 9y – 20z = - 4;

4x – 15y + 10z = - 1;

2x - 3y - 5z = - 1.

Solve each of the following systems of equations using matrix method.

3x - 4y + 2z = - 1;

2x + 3y + 5z = 7;

X + z = 2.

Solve each of the following systems of equations using matrix method.

X + y - z = 1;

3x + y – 2z = 3;

X – y – z = - 1.

Solve each of the following systems of equations using matrix method.

2x + y - z = 1;

x – y + z = 2;

3x + y – 2z = - 1.

Solve each of the following systems of equations using matrix method.

X + 2y + z = 4;

- x + y + z = 0;

x - 3y + z = 4.

Solve each of the following systems of equations using matrix method.

x - y – 2z = 3;

x + y = 1;

x + z = - 6.

Solve each of the following systems of equations using matrix method.

5x - y = - 7;

2x + 3z = 1;

3y – z = 5.

Solve each of the following systems of equations using matrix method.

x - 2y + z = 0;

y – z = 2;

2x – 3z = 10.

Solve each of the following systems of equations using matrix method.

x - y = 3;

2x + 3y + 4z = 17;

y + 2z = 7.

Solve each of the following systems of equations using matrix method.

4x + 3y + 2z = 60;

x + 2y + 3z = 45;

6x + 2y + 3z = 70.

If A = , find A ^{- 1}.

Using A ^{- 1}, solve the following system of equations:

2x – 3y + 5z = 11;

3x + 2y – 4z = - 5;

x + y – 2z = - 3.

If A = , find A ^{- 1}.

Using A ^{- 1}, solve the following

system of linear equations:

2x + y + z = 1;

X – 2y – z = ;

3y – 5z = 9.

HINT: Here A = ,

X = and B = .

If A = and

B = , find AB.

Hence, solve the system of equations:

x – 2y = 10,

2x + y + 3z = 8 and

- 2y + z = 7.

HINT: AB = (11)I = A = I

A ^{- 1} = B.

= 10, = 10,

= 13

Ans. x = , y = , z =

= 4; = 0;

= 2. (x, y, z ≠ 0)

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

The cost of 4 kg potato, 3 kg wheat and 2 kg of rice is ₹ 60. The cost of 1 kg potato, 2 kg wheat and 3 kg of rice is ₹45. The cost of 6 kg potato, 2 kg wheat and 3 kg of rice is ₹70. Find the cost of each item per kg by matrix method.

An amount of ₹ 5000 is put into three investments at 6%, 7% and 8% per annum respectively. The total annual income from these investments is ₹358. If the total annual income from first two investments is ₹70more

than the income from the third, find the amount of each investment by the matrix method.

HINT: Let these investments be ₹x, ₹y and ₹z, respectively.

Then, x + y + z = 5000, …(i)

= 358

6x + 7y + 8z = 35800 …(ii)

And,

6x + 7y - 8z = 7000. …(iii)

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 ₹ 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.

HINT: By the given data, we have

If A and B are 2-rowed square matrices such that

If + 2A =then A=?

If A=and B=are such that 4A + 3X = 5B then X=?

If (A-2B)=and (2A-3B) =then B=?

If (2A – B) = and (2B + A) =then A=?

If 2+=

If=then

If=then

If the matrix A =is singular then x=?

If A_α =then (A_α)²=?

If A =be such that A + A^’ = I, then α =?

If A=is singular then k=?

If A =then adj A=?

If A =and A^-1=then x=?

If A and B are square matrices of the same order then (A + B)(A – B) = ?

If A and B are square matrices of the same order then (A + B)² =?

If A and B are square matrices of the same order then (A – B)² =?

If A and B are symmetric matrices of the same order then (AB – BA) is always

Matrices A and B are inverse of each other only when

For square matrices A and B of the same order, we have adj(AB)=?

If A is a 3-rowed square matrix and │A│=4 then adj(adj A)=?

If A is a 3-rowed square matrix and │A│=5 then │adj A│=?

For any two matrices A and B,

If A =then A=?

If A is an invertible square matrix then │A^-1│=?

If A and B are invertible matrices of the same order then (AB)^-1=?

If A and B are two nonzero square matrices of the same order such that AB=0 then

If A is a square matrix such that │A│≠0 and A² – A + 2I = 0 then A^-1=?

If A=is not invertible then λ=?

If A=then A^-1=?

The matrix A=is

The matrix A=is

If A is singular then A(adjA)=?

For any 2-rowed square matrix A, if A(adjA) = then the value of │A│ is

If A =then │A^-1│=?

If A =and A² + xI = yA then the values of x and y are

If matrices A and B anticommute then

If A =then adj A=?

If A = and B is a square matrix of order 2 such that AB=I then B=?

If A and B are invertible square matrices of the same order then (AB)^-1=?

If A=, then A^-1=?

If │A│=3 and A^-1=then adj A=?

If A is an invertible matrix and A^-1 = then A=?

If A= and ƒ(x)=2x² – 4x + 5 then ƒ(A)=?

If A= then A² – 4A = ?

If A is a 2-rowed square matrix and │A│=6 then =?

If A is an invertible square matrix and k is a non-negative real number then (KA)^-1=?

If A=then A^-1=?

If A is a square matrix then (A + A^’) is

If A is a square matrix then (A-A^’) is

If A is a 3-rowed square matrix and │3A│=k │A│ then k =?

Which one of the following is a scalar matrix?

If A=and B= and

(A + B)² = (A² + B²) then