Advertisements
Advertisements
प्रश्न
The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.
विकल्प
`[(4, 8, 3),(2, 1,6),(0, 2, 1)]`
`[(1, -1, 0),(-2, 3, -4),(-2, 3, -3)]`
`[(11, 9, 3),(1, 2, 8),(6, 9, 1)]`
`[(1, -2, 1),(-1, 3, 3),(-2, 3, -3)]`
उत्तर
The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is `bbunderline([(1, -1, 0),(-2, 3, -4),(-2, 3, -3)])`.
Explanation:
`M_11 = |(-3, 4), (-1, 1) = -3 + 4 = 1|`
`M_12 = |(2, 4), (0, 1)| = 2 + 0 = 2`
`M_13 = |(2, -3), (0, -1)| = -2 + 0 = -2`
`M_21 = |(-3, -1), (-1, 1)| = -3 + 4 = 1`
`M_22 = |(3, 4), (0, 1)| = 3 - 0 = 3`
`M_23 = |(3, -3), (0, -1)| = -3 + 0 = 3`
`M_31 = |(-3, 4), (-3, 4)| = 12 - 8 = 4`
`M_32 = |(3, 4), (2, 4)| = 12 - 8 = 4`
`M_33 = |(3, -3), (2, -3)| = -9 + 6 = 3`
A11 = −1
A12 = −2
A13 = −2
A21 = −1
A22 = 3
A23 = 3
A31 = 0
A32 = −4
A33 = −3
[Cofactor A] = `[(-1, -2, -2), (-1, 3, 3), (0, -4, -3)]`
Adj (A) = (Cof A)T
`[(-1, -1, 0), (-2, 3, -4), (-2, 3, -3)]`
APPEARS IN
संबंधित प्रश्न
Find the co-factor of the element of the following matrix:
`[(-1, 2),(-3, 4)]`
Find the adjoint of the following matrix.
`[(2,-3),(3,5)]`
Find the inverse of the following matrix by the adjoint method.
`[(-1,5),(-3,2)]`
Find the inverse of the following matrix.
`[(1,2),(2,-1)]`
Find the inverse of the following matrix.
`[(2, -3),(-1, 2)]`
Find the inverse of the following matrix.
`[(2,0,-1),(5,1,0),(0,1,3)]`
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
Check whether the following matrices are invertible or not:
`[(1, 1),(1, 1)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(1, -1),(2, 3)]`
If A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______
If A = `[(cos alpha, sin alpha),(-sin alpha, cos alpha)]`, then A10 = ______
If A = `[(4, 5),(2, 5)]`, then |(2A)−1| = ______
For an invertible matrix A, if A . (adj A) = `[(10, 0),(0, 10)]`, then find the value of |A|.
A = `[(cos theta, - sin theta),(-sin theta, -cos theta)]` then find A−1
If A = `[("a", "b"),("c", "d")]` then find the value of |A|−1
A + I = `[(3, -2),(4, 1)]` then find the value of (A + I)(A − I)
If A = [aij]2×2, where aij = i – j, then A = ______
The value of Cofactor of element a21 in matrix A = `[(1, 2),(5, -8)]` is ______
Find the adjoint of the matrix A = `[(2,3),(1,4)]`
Find the inverse of the following matrix:
`[(1,-1),(2,3)]`
Find the inverse of the following matrix:
`[(3,1),(-1,3)]`
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.
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 = `[(a,b),(c,d)]` such that ad - bc ≠ 0 then A-1 is
Which of the following matrix has no inverse
The cost of 2 Kg of Wheat and 1 Kg of Sugar is ₹ 70. The cost of 1 Kg of Wheat and 1 Kg of Rice is ₹ 70. The cost of 3 Kg of Wheat, 2 Kg of Sugar and 1 Kg of rice is ₹ 170. Find the cost of per kg each item using the matrix inversion method.
If A = `[(2, 0, -1), (5, 1, 0), (0, 1, 3)]` and A−1 = `[(3, -1, 1), (α, 6, -5), (β, -2, 2)]`, then the values of α and β are, respectively.
If [abc] ≠ 0, then `(["a" + "b b" + "c c" + "a"])/(["b c a"])` = ____________.
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A2 - A + I = 0, then A-1 = ______.
If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = ______.
The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible ______.
The number of solutions of equation x2 – x3 = 1, – x1 + 2x3 = 2, x1 – 2x2 = 3 is ______.
The inverse of the matrix `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]` is ______.
For a invertible matrix A if A(adjA) = `[(10, 0),(0, 10)]`, then |A| = ______.
If A and B are two square matrices such that A2B = BA and (AB)10 = AkB10. Then, k is ______.
If A = `[(3, 1),(-1, 2)]`, show that A2 – 5A + 7I = 0
