Advertisements
Advertisements
प्रश्न
Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`
Advertisements
उत्तर
`A = [(2,-3),(-4,7)]`
|A| = 14 - 12 = 2
`:. A_11 = 7` `A_12 = 4` `A_31 = 3` `A_22 = 2`
`adj(A) = [(A_11,A_22),(A_21,A_22)]^T = [(7,4),(3,2 )]^T = [(7,3),(4,2)]`
`:. A^(-1) = I/(|A|) adj (A) = 1/2 [(7,3),(4,2)]`
L.H.S = `2A^(-1) = [(7,3),(4,2)]`
R.H.S = `9I - A = [(9,0),(0,9)] - [(2,-3),(-4,7)] = [(7,3),(4,2)]`
L.H.S = R.H.S
APPEARS IN
संबंधित प्रश्न
If for any 2 x 2 square matrix A, `A("adj" "A") = [(8,0), (0,8)]`, then write the value of |A|
Find the value of x, y, and z from the following equation:
`[(x+y+z), (x+z), (y+z)] = [(9),(5),(7)]`
`A = [a_(ij)]_(mxxn)` is a square matrix, if ______.
If A = `[(alpha, beta),(gamma, -alpha)]` is such that A2 = I then ______.
Let A = `((2,-1),(3,4))`, B = `((5,2),(7,4))`, C= `((2,5),(3,8))` find a matrix D such that CD − AB = O
A coaching institute of English (subject) conducts classes in two batches I and II and fees for rich and poor children are different. In batch I, it has 20 poor and 5 rich children and total monthly collection is Rs 9,000, whereas in batch II, it has 5 poor and 25 rich children and total monthly collection is Rs 26,000. Using matrix method, find monthly fees paid by each child of two types. What values the coaching institute is inculcating in the society?
Show that (A + A') is symmetric matrix, if `A = ((2,4),(3,5))`
If A is a square matrix of order 3 with |A| = 4 , then the write the value of |-2A| .
if `vec"a"= 2hat"i" + 3hat"j"+ hat"k", vec"b" = hat"i" -2hat"j" + hat"k" and vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`
Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:
`[(10, -15, 27),(-15, 0, sqrt(34)),(27, sqrt(34), 5/3)]`
Identify the following matrix is singular or non-singular?
`[("a", "b", "c"),("p", "q", "r"),(2"a" - "p", 2"b" - "q", 2"c" - "r")]`
Identify the following matrix is singular or non-singular?
`[(7, 5),(-4, 7)]`
Answer the following question:
If A = `[(1, omega),(omega^2, 1)]`, B = `[(omega^2, 1),(1, omega)]`, where ω is a complex cube root of unity, then show that AB + BA + A −2B is a null matrix
If A = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.
State whether the following statement is True or False:
If A is non singular, then |A| = 0
If A is a square matrix of order 2 such that A(adj A) = `[(7, 0),(0, 7)]`, then |A| = ______
If two matrices A and B are of the same order, then 2A + B = B + 2A.
If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2
If A is a square matrix, then A – A’ is a ____________.
If A is a square matrix such that A2 = A, then (I + A)2 - 3A is ____________.
A = `[a_(ij)]_(m xx n)` is a square matrix, if
The number of all possible matrices of order 3/3, with each entry 0 or 1 is
If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to
If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.
Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A100B = BA100
Reason: AB = BA implies AB = BA for all positive integers n.
