Advertisements
Advertisements
प्रश्न
If A = `[("a", "b"),("c", "d")]` then find the value of |A|−1
उत्तर
|A| = `|("a", "b"),("c", "d")|`
= ad – bc
∴ |A|−1 = `1/("ad" - "bc")` .......`[∵ |"A"^-1| = 1/|"A"|]`
APPEARS IN
संबंधित प्रश्न
Find the inverse of the following matrix by the adjoint method.
`[(2,-2),(4,3)]`
Find AB, if A = `((1,2,3),(1,-2,-3))` and B = `((1,-1),(1,2),(1,-2))`. Examine whether AB has inverse or not.
Find the inverse of the following matrix (if they exist):
`[(2,0,-1),(5,1,0),(0,1,3)]`
Choose the correct answer from the given alternatives in the following question:
If A = `[(2,-4),(3,1)]`, then the adjoint of matrix A is
Choose the correct answer from the given alternatives in the following question:
If A−1 = `- 1/2[(1,-4),(-1,2)]`, then A = ______.
Find the inverse of the following matrices by the adjoint method `[(2, -2),(4, 5)]`.
If A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)] "and B" = [(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find a matrix X such that XA = B.
Adjoint of `[(2, -3),(4, -6)]` is _______
Fill in the blank :
If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = _______
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 :
`[(2, 0, -1),(5, 1, 0),(0, 1, 3)]`
A = `[(cos alpha, - sin alpha, 0),(sin alpha, cos alpha, 0),(0, 0, 1)]`, then A−1 is
If A = `[(4, 5),(2, 5)]`, then |(2A)−1| = ______
Find A–1 using adjoint method, where A = `[(cos theta, sin theta),(-sin theta, cos theta)]`
If A = `[(0, 1),(2, 3),(1, -1)]` and B = `[(1, 2, 1),(2, 1, 0)]`, then find (AB)−1
The value of Minor of element b22 in matrix B = `[(2, -2),(4, 5)]` is ______
Find the inverse of the following matrix:
`[(3,1),(-1,3)]`
Find the inverse of the following matrix:
`[(-3,-5,4),(-2,3,-1),(1,-4,-6)]`
If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.
Find m if the matrix `[(1,1,3),(2,λ,4),(9,7,11)]` has no inverse.
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.
The inverse matrix of `((4/5,(-5)/12),((-2)/5,1/2))` is
The matrix A = `[("a",-1,4),(-3,0,1),(-1,1,2)]` is not invertible only if a = _______.
If A = `[(x,1),(1,0)]` and A = A , then x = ______.
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 = `[(1 + 2"i", "i"),(- "i", 1 - 2"i")]`, where i = `sqrt-1`, then A(adj A) = ______.
If A = `[(0, 0, 1), (0, 1, 0), (1, 0, 0)]`, then A-1 = ______
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A = `[(cos theta, sin theta, 0),(-sintheta, costheta, 0),(0, 0, 1)]`, where A11, A11, A13 are co-factors of a11, a12, a13 respectively, then the value of a11A11 + a12A12 + a13A13 = ______.
If A, B are two square matries, such that AB = B, BA = A and n ∈ N then (A + B)n =
If matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A–1 = `1/k` (adj A), then k is ______.
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 ______.
If A = `[(cos α, sin α),(-sin α, cos α)]`, then find α satisfying `0 < α < π/2`, when A + AT = `sqrt(2) l_2` where AT is transpose of A.
If A = `[(cos α, sin α),(- sin α, cos α)]`, then the matrix A is ______.
If A = `[(1, 2, 4),(4, 3, -2),(1, 0, -3)]`. Show that A–1 exists and find A–1 using column transformation.
