Advertisements
Advertisements
प्रश्न
Solve the following equations by inversion method.
2x + 6y = 8, x + 3y = 5
Advertisements
उत्तर
The given equations can be written in the matrix form as:
`[(2,6),(1,3)][("x"),("y")]=[(8),(5)]`
This is of the form AXB, where
A = `[(2,6),(1,3)]`, X = `[("x"),("y")]` and B = `[(8),(5)]`
Let us find A−1
|A| = `[(2,6),(1,3)]` = 6 − 6 = 0
∴ A−1 does not exist.
Hence, x and y do not exist.
APPEARS IN
संबंधित प्रश्न
Solve the following equations by the reduction method.
2x + y = 5, 3x + 5y = – 3
Solve the following equations by the reduction method.
3x – y = 1, 4x + y = 6
Solve the following equations by the reduction method.
5x + 2y = 4, 7x + 3y = 5
Solve the following equations by inversion method:
x + y = 4, 2x – y = 5
Solve the following equation by the method of inversion:
2x - y = - 2, 3x + 4y = 3
Solve the following equations by the method of inversion:
x + y+ z = 1, 2x + 3y + 2z = 2,
ax + ay + 2az = 4, a ≠ 0.
Express the following equations in matrix form and solve them by the method of reduction:
`x + y = 1, y + z = 5/3, z + x 4/33`.
Express the following equations in matrix form and solve them by the method of reduction:
2x - y + z = 1, x + 2y + 3z = 8, 3x + y - 4z = 1.
Express the following equations in matrix form and solve them by the method of reduction:
x + 2y + z = 8, 2x + 3y – z = 11, 3x – y – 2z = 5.
The cost of 4 pencils, 3 pens, and 2 books is ₹ 150. The cost of 1 pencil, 2 pens, and 3 books is ₹ 125. The cost of 6 pencils, 2 pens, and 3 books is ₹ 175. Find the cost of each item by using matrices.
An amount of ₹ 5000 is invested in three types of investments, at interest rates 6%, 7%, 8% per annum respectively. The total annual income from these investments is ₹ 350. If the total annual income from the first two investments is ₹ 70 more than the income from the third, find the amount of each investment using matrix method.
Solve the following equations by the method of inversion:
2x + 3y = - 5, 3x + y = 3
Express the following equations in matrix form and solve them by the method of reduction:
x + 3y + 2z = 6,
3x − 2y + 5z = 5,
2x − 3y + 6z = 7
Solve the following equations by method of inversion:
x + y + z = 1, x – y + z = 2 and x + y – z = 3
Express the following equations in matrix form and solve them by method of reduction.
3x – y = 1, 4x + y = 6
Express the following equations in matrix form and solve them by the method of reduction.
x + y + z = 1, 2x + 3y + 2z = 2 and x + y + 2z = 4
The total cost of 3 T.V. and 2 V.C.R. is ₹ 35,000. The shopkeeper wants profit of ₹1000 per television and ₹ 500 per V.C.R. He can sell 2 T.V. and 1 V.C.R. and get the total revenue as ₹ 21,500. Find the cost price and the selling price of a T.V. and a V.C.R.
If x + y + z = 3, x + 2y + 3z = 4, x + 4y + 9z = 6, then (y, z) = _______
Solve the following equations by method of inversion : x + y – z = 2, x – 2y + z = 3 and 2x – y – 3z = – 1
Solve the following equations by method of reduction:
x + 2y + z = 3, 3x – y + 2z = 1 and 2x – 3y + 3z = 2
Solve the following equations by method of reduction :
x – 3y + z = 2 , 3x + y + z = 1 and 5x + y + 3z = 3
The sum of three numbers is 6. If we multiply third number by 3 and add it to the second number we get 11. By adding the first and third number we get a number which is double the second number. Use this information and find a system of linear equations. Find the three numbers using matrices.
If A2 + 5A + 3I = 0, |A| ≠ 0, then A–1 = ______
Complete the following activity.
The cost of 4 kg potato, 3kg wheat and 2kg rice is ₹ 60. The cost of 1 kg potato, 2 kg wheat and 3kg rice is ₹ 45. The cost of 6 kg potato, 3 kg rice and 2 kg wheat is ₹ 70. Find the per kg cost of each item by matrix method.
Solution: Let the cost of potato, wheat and rice per kg be x, y and z respectively.
Therefore by given conditions,
4x + ( )y + 2( ) = ( )
x + 2y + ( )( ) = ( )
( )x + 2y + 3z = ( )
Matrix form of above equations is,
`[("( )", 3, "( )"),(1, "( )", 3),("( )", 2, "( )")] [(x),(y),(z)] =[("( )"), (45), ("( )")]`
R1 ↔ R2
`[(1, 2, 3),("( )", "( )", "( )"),(6, 2, 3)] [(x),(y),(z)] =[("( )"), (60), ("( )")]`
R2 – 4R1, R3 – 6R1
`[(1, 2, 3),("( )", -5, "( )"),(0, "( )", -15)] [(x),(y),(z)] =[(45), ("( )"), (-200)]`
`(-1)/5 "R"_2, (-1)/5 "R"_3`
`[("( )", 2, 3),(0, "( )", 2),(0, 2, "( )")] [(x),("( )"),(z)] =[(45), (24), (40)]`
R3 – 2R2
`[(1, 2, 3),(0, 1, 2),(0, 0, -1)] [(x),(y),(z)] =[("( )"), ("( )"), ("( )")]`
By pre multiplying we get,
x + 2y + ( )z = ( ) .....(i)
y + 2z = 24 ......(ii)
–z = ( ) ......(iii)
From (iii), we get, z = ( )
From (ii), we get, y = ( )
From (i), we get, x = ( )
Therefore the cost of Potato, Wheat and Rice per kg are _______, _______ and _______ respectively.
If the volume of the parallelepiped whose conterminus edges are along the vectors a, b, c is 12, then the volume of the tetrahedron whose conterminus edges are a + b, b + c and c + a is ______.
If A = `[(1, -1, 3), (2, 5, 4)]`, then R1 ↔ R2 and C3 → C3 + 2C2 gives ______
If `[(1, -1, x), (1, x, 1), (x, -1, 1)]` has no inverse, then the real value of x is ______
If A =`[(1, -1), (2, 3)]` and adj (A) = `[(a, b), (-2, 1)]`, then ______
Solve the following system of equations by the method of reduction:
x + y + z = 6, y + 3z = 11, x + z = 2y.
