Advertisements
Advertisements
प्रश्न
If A is a 3 × 3 invertible matrix, then what will be the value of k if det(A–1) = (det A)k
Advertisements
उत्तर
For any invertible square matrix A, the determinant of its inverse is given by:
`det(A^-1) = 1/det(A)`
`1/det(A) = (detA)^k`
(det A)−1 = (det A)k ⇒ k = −1
k = −1
APPEARS IN
संबंधित प्रश्न
A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received Rs 2,800 as interest. However, if trust had interchanged money in bonds, they would have got Rs 100 less as interest. Using matrix method, find the amount invested by the trust. Interest received on this amount will be given to Helpage India as donation. Which value is reflected in this question?
Find the inverse of each of the matrices, if it exists. [`(1, -1),(2,3)`]
Find the inverse of each of the matrices, if it exists.` [(2,1),(1,1)]`
Find the inverse of each of the matrices, if it exists.
`[(1,3),(2,7)]`
Find the inverse of each of the matrices, if it exists.
`[(2,3),(5,7)]`
Find the inverse of each of the matrices, if it exists.
`[(2,7),(1,4)]`
Find the inverse of each of the matrices, if it exists.
`[(4,5),(3,4)]`
`Find the inverse of each of the matrices, if it exists.
`[(3,-1),(-4,2)]`
Find the inverse of each of the matrices, if it exists.
`[(2, -6),(1, -2)]`
Find the inverse of each of the matrices, if it exists.
`[(6,-3),(-2,1)]`
Find the inverse of each of the matrices, if it exists.
`[(2,1),(4,2)]`
Find the inverse of each of the matrices, if it exists.
`[(1,3,-2),(-3,0,-5),(2,5,0)]`
Find the inverse of each of the matrices, if it exists.
`[(2,0,-1),(5,1,0),(0,1,3)]`
Find the inverse of each of the matrices, if it exists.
`[(1,3,-2),(-3,0,-5),(2,5,0)]`
Find the inverse of each of the matrices, if it exists.
`[(2,0,-1),(5,1,0),(0,1,3)]`
Two schools P and Q want to award their selected students on the values of tolerance, kindness and leadership. School P wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3, 2 and 1 students, respectively, with a total award money of Rs 2,200. School Q wants to spend Rs 3,100 to award 4, 1 and 3 students on the respective values (by giving the same award money to the three values as school P). If the total amount of award for one prize on each value is Rs 1,200, using matrices, find the award money for each value.
Find inverse, by elementary row operations (if possible), of the following matrices
`[(1, 3),(-5, 7)]`
Find inverse, by elementary row operations (if possible), of the following matrices
`[(1, -3),(-2, 6)]`
If A and B are invertible matrices of the same order, then (AB)-1 is equal to ____________.
If A, B are non-singular square matrices of the same order, then (AB–1)–1 = ______.
