Advertisements
Advertisements
Question
Choose the correct answer from the given alternatives in the following question:
If A = `[("cos"alpha, - "sin"alpha,0),("sin"alpha,"cos"alpha,0),(0,0,1)]` where α ∈ R, then [F(α)]-1 is
Options
F(- α)
F(α-1)
F(2α)
none of these
Solution
F(- α)
APPEARS IN
RELATED QUESTIONS
If A = `[(1, 3), (3, 1)]`, Show that A2 - 2A is a scalar matrix.
Solve the following equations by the inversion method :
2x + 3y = - 5 and 3x + y = 3.
Find the co-factor of the element of the following matrix.
`[(1,-1,2),(-2,3,5),(-2,0,-1)]`
Find the matrix of the co-factor for the following matrix.
`[(1,3),(4,-1)]`
Find the inverse of the following matrix.
`[(1,2),(2,-1)]`
Find the inverses of the following matrices by the adjoint method:
`[(1,2,3),(0,2,4),(0,0,5)]`
Find the inverse of the following matrix (if they exist):
`((1,-1),(2,3))`
Find the inverse of the following matrix (if they exist):
`[(2,1),(7,4)]`
Find the inverse of the following matrix (if they exist):
`[(2,-3,3),(2,2,3),(3,-2,2)]`
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 = `[(lambda,1),(-1, -lambda)]`, and A-1 does not exist if λ = _______
Find the inverse of the following matrices by transformation method:
`[(2, 0, −1),(5, 1, 0),(0, 1, 3)]`
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 _______
Choose the correct alternative.
If A is a 2 x 2 matrix such that A(adj. A) = `[(5, 0),(0, 5)]`, then |A| = _______
The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.
`cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______
If A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find the value of a31A31 + a32A32 + a33A33.
If A = `[(3, 1),(5, 2)]`, and AB = BA = I, then find the matrix B
Find the adjoint of matrix A = `[(6, 5),(3, 4)]`
The value of Cofactor of element a21 in matrix A = `[(1, 2),(5, -8)]` is ______
Complete the following activity to verify A. adj (A) = det (A) I.
Given A = `[(2, 0, -1),(5, 1, 0),(0, 1, 3)]` then
|A| = 2(____) – 0(____) + ( ) (____)
= 6 – 0 – 5
= ______ ≠ 0
Cofactors of all elements of matrix A are
A11 = `(-1)^2 |("( )", "( )"),("( )", "( )")|` = (______),
A12 = `(-1)^3 |(5, "( )"),("( )", 3)|` = – 15,
A13 = `(-1)^4 |(5, "( )"),("( )", 1)|` = 5,
A21 = _______, A22 = _______, A23 = _______,
A31 = `(-1)^4 |("( )", "( )"),("( )", "( )")|` = (______),
A32 = `(-1)^5 |(2, "( )"),("( )", 0)|` = ( ),
A33 = `(-1)^6 |(2, "( )"),("( )", 1)|` = 2,.
Cofactors of matrix A = `[(3, "____", "____"),("____", "____",-2),(1, "____", "____")]`
adj (A) = `[("____", "____", "____"),("____", "____","____"),("____","____","____")]`
A.adj (A) = `[(2, 0, -1),(5, 1, 0),(0, 1, 3)] [("( )", -1, 1), (-15, "( )", -5),("( )", -2, "( )")] = [(1, 0, "( )"),("( )", "( )", "( )"),(0, "( )", "( )")]` = |A|I
Find the adjoint of the matrix A = `[(2,3),(1,4)]`
If A = `[(1,3,3),(1,4,3),(1,3,4)]` then verify that A(adj A) = |A| I and also find A-1.
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:
2x – z = 0; 5x + y = 4; y + 3z = 5
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.
Which of the following matrix has no inverse
If A = `|(1,1,1),(3,4,7),(1,-1,1)|` verify that A(adj A) = (adj A)(A) = |A|I3.
Solve by using matrix inversion method:
x - y + z = 2, 2x - y = 0, 2y - z = 1
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 = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, then B-1A-1 = ?
If A–1 = `[(3, -1, 1),(-15, 6, -5),(5, -2, 2)]`, then adj A = ______.
Choose the correct option:
If X, Y, Z are non zero real numbers, then the inverse of matrix A = `[(x, 0, 0),(0, y, 0),(0, 0, z)]`
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 ______.