Advertisements
Advertisements
प्रश्न
If A = `[(0, 0, -1),(0, -1, 0),(-1, 0, 0)]`, then the only correct statement about the matrix A is ______
पर्याय
A2 = I
A is a zero matrix
A−1 does not exit
A = (−1) I, where I is a unit matrix
उत्तर
A2 = I
APPEARS IN
संबंधित प्रश्न
Find the co-factor of the element of the following matrix.
`[(1,-1,2),(-2,3,5),(-2,0,-1)]`
If A = `[(1,-1,2),(3,0,-2),(1,0,3)]` verify that A (adj A) = (adj A) A = | A | I
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):
`((1,3),(2,7))`
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 = _______
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
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
If A = `[(1, 2),(-3, -1)], "B" = [(-1, 0),(1, 5)]`, then AB =
Fill in the blank :
If A = [aij]mxm is a non-singular matrix, then A–1 = `(1)/(......)` adj(A).
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, 1),(7, 4)]`
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 the inverse of the matrix `[(alpha, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exists then find the value of α
If A = `[(2, 2),(-3, 2)]` and B = `[(0, -1),(1, 0)]`, then find the matrix (B−1 A−1)−1.
If A(α) = `[(cos alpha, sin alpha),(-sin alpha, cos alpha)]` then prove that A2(α) = A(2α)
If A = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)]` and B = `[(x),(y),(z)]`, find the matrix B'(AB)
If A = `[(-1),(2),(3)]`, B = `[(3, 1, -2)]`, find B'A'
State whether the following statement is True or False:
Inverse of `[(2, 0),(0, 3)]` is `[(1/2, 0),(0, 1/3)]`
The value of Minor of element b22 in matrix B = `[(2, -2),(4, 5)]` 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
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.
If A = `[(1,2),(3,-5)]`, then A-1 = ?
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 A is non-singular matrix such that (A - 2l)(A - 4l) = 0 then A + 8A-1 = ______.
If A is a solution of x2 - 4x + 3 = 0 and `A=[[2,-1],[-1,2]],` then A-1 equals ______.
If A = `[(2, 2),(4, 5)]` and A–1 = λ(adj(A)), then λ = ______ .
If matrix A = `[(1, -1),(2, 3)]` such that AX = I, then X is equal to ______.
If A = `[(2, 3),(a, 6)]` is a singular matrix, then a = ______.
Find the inverse of the matrix A by using adjoint method.
where A = `[(-3, -1, 1),(0, 0, 1),(-15, 6, -6)]`
A–1 exists if |A| = 0.
If A = `[(x, 1),(1, 0)]` and A = A–1, then x = ______.
Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.
For a invertible matrix A if A(adjA) = `[(10, 0),(0, 10)]`, then |A| = ______.
If A = `[(1, 2),(3, 4)]` verify that A (adj A) = (adj A) A = |A| I
if `A = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.
If A = `[(3, 1),(-1, 2)]`, show that A2 – 5A + 7I = 0
