Advertisements
Advertisements
प्रश्न
Find the inverse of the following matrix (if they exist):
`((1,-1),(2,3))`
उत्तर
Let A = `((1,-1),(2,3))`
∴ |A| = `|(1,-1),(2,3)| = 3 + 2 = 5 ≠ 0`
∴ A-1 exists.
Consider AA-1 = I
∴ `((1,-1),(2,3)) "A"^-1 = ((1,0),(0,1))`
By R2 - 2R1, we get,
`((1,-1),(0,5)) "A"^-1 = ((1,0),(-2,1))`
By `(1/5) "R"_2`, we get,
`((1,-1),(0,1)) "A"^-1 = ((1,0),(-2/5,1/5))`
By R1 + R2, we get,
`((1,0),(0,1)) "A"^-1 = ((3/5,1/5),(-2/5,1/5))`
∴ A-1 = `1/5((3,1),(-2,1))`
APPEARS IN
संबंधित प्रश्न
Find the matrix of the co-factor for the following matrix.
`[(1, 0, 2),(-2, 1, 3),(0, 3, -5)]`
Find the inverse of the following matrix by the adjoint method.
`[(1, 0, 0),(3, 3, 0),(5, 2, -1)]`
Find the inverse of the following matrix (if they exist):
`((1,3),(2,7))`
Choose the correct answer from the given alternatives in the following question:
If A = `[(lambda,1),(-1, -lambda)]`, and A-1 does not exist if λ = _______
Choose the correct answer from the given alternatives in the following question:
The inverse of A = `[(0,1,0),(1,0,0),(0,0,1)]` is
Find the inverse of the following matrices by the adjoint method `[(3, -1),(2, -1)]`.
Find the inverse `[(1, 2, 3 ),(1, 1, 5),(2, 4, 7)]` of the elementary row tranformation.
Choose the correct alternative.
If A is a 2 x 2 matrix such that A(adj. A) = `[(5, 0),(0, 5)]`, then |A| = _______
Fill in the blank :
If A = [aij]mxm is a non-singular matrix, then A–1 = `(1)/(......)` adj(A).
State whether the following is True or False :
If A and B are conformable for the product AB, then (AB)T = ATBT.
State whether the following is True or False :
Singleton matrix is only row matrix.
State whether the following is True or False :
A(adj. A) = |A| I, where I is the unit matrix.
Check whether the following matrices are invertible or not:
`[(1, 0),(0, 1)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(1, -1),(2, 3)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, -3, 3),(2, 2, 3),(3, -2, 2)]`
If A = `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`, find adj (A).
Find the inverse of the following matrix:
`[(-3,-5,4),(-2,3,-1),(1,-4,-6)]`
If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)
If A = `[(-1,2,-2),(4,-3,4),(4,-4,5)]` then, show that the inverse of A is A itself.
If X = `[(8,-1,-3),(-5,1,2),(10,-1,-4)]` and Y = `[(2,1,-1),(0,2,1),(5,p,q)]` then, find p, q if Y = X-1
Solve by matrix inversion method:
2x + 3y – 5 = 0; x – 2y + 1 = 0.
Solve by matrix inversion method:
x – y + 2z = 3; 2x + z = 1; 3x + 2y + z = 4
A sales person Ravi has the following record of sales for the month of January, February and March 2009 for three products A, B and C. He has been paid a commission at fixed rate per unit but at varying rates for products A, B and C.
| Months | Sales in units | Commission | ||
| A | B | C | ||
| January | 9 | 10 | 2 | 800 |
| February | 15 | 5 | 4 | 900 |
| March | 6 | 10 | 3 | 850 |
Find the rate of commission payable on A, B and C per unit sold using matrix inversion method.
The sum of three numbers is 20. If we multiply the first by 2 and add the second number and subtract the third we get 23. If we multiply the first by 3 and add second and third to it, we get 46. By using the matrix inversion method find the numbers.
Weekly expenditure in an office for three weeks is given as follows. Assuming that the salary in all the three weeks of different categories of staff did not vary, calculate the salary for each type of staff, using the matrix inversion method.
| Week | Number of employees | Total weekly salary (in ₹) |
||
| A | B | C | ||
| 1st week | 4 | 2 | 3 | 4900 |
| 2nd week | 3 | 3 | 2 | 4500 |
| 3rd week | 4 | 3 | 4 | 5800 |
If A is 3 × 3 matrix and |A| = 4 then |A-1| is equal to:
If A = `[(1,2),(3,-5)]`, then A-1 = ?
If [abc] ≠ 0, then `(["a" + "b b" + "c c" + "a"])/(["b c a"])` = ____________.
If A = `[(p/4, 0, 0), (0, q/5, 0), (0, 0, r/6)]` and `"A"^-1 = [(1/4, 0, 0), (0, 1/5, 0), (0, 0, 1/6)]`, then p + q + r = ______
If A = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is ______
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
If A, B are two square matries, such that AB = B, BA = A and n ∈ N then (A + B)n =
If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A2 – 5A)A–1 = ______.
The inverse of the matrix `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]` is ______.
If the inverse of the matrix `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exist, then the value of α is ______.
If matrix A = `[(1, 2),(4, 3)]`, such that AX = I, then X is equal to ______.
For an invertible matrix A, if A (adj A) = `|(20, 0),(0, 20)|`, then | A | = ______.
If A = `[(3, 1),(-1, 2)]`, show that A2 – 5A + 7I = 0
