Advertisements
Advertisements
प्रश्न
Choose the correct alternative.
If A2 + mA + nI = O and n ≠ 0, |A| ≠ 0, then A–1 = _______
पर्याय
`(-1)/"m"("A" + "nI")`
`(-1)/"n"("A" + "mI")`
`(-1)/"n"("I" + "mA")`
(A + mnI)
उत्तर
A2 + mA + nI = O
∴ A–1A2 + mA–1A + n A–1 I = 0
∴ (A–1 A)A + mI + n A–1 = 0
∴ IA + mI + nA–1 = 0
∴ A–1 = `(-1)/"n"("A" + "mI")`.
APPEARS IN
संबंधित प्रश्न
Find the adjoint of the following matrix.
`[(1, -1, 2),(-2, 3, 5),(-2, 0, -1)]`
Find the inverse of the following matrix.
`[(1,2),(2,-1)]`
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,-3),(5,7)]`
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:
The inverse of A = `[(0,1,0),(1,0,0),(0,0,1)]` is
Find the inverse of the following matrices by the adjoint method `[(2, -2),(4, 5)]`.
Find the inverse of the following matrices by transformation method: `[(1, 2),(2, -1)]`
Fill in the blank :
If a1x + b1y = c1 and a2x + b2y = c2, then matrix form is `[(......, ......),(......, ......)] = [(x),(y)] = [(......),(......)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(1, -1),(2, 3)]`
The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.
If A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______
If `[(x - y - z),(-y + z),(z)] = [(0),(5),(3)]`, then the value of x, y and z are respectively ______
If A is invertible matrix of order 3 and |A| = 5, then find |adj A|
Find A–1 using adjoint method, where A = `[(cos theta, sin theta),(-sin theta, cos theta)]`
Find the adjoint of matrix A = `[(6, 5),(3, 4)]`
Find the adjoint of matrix A = `[(2, 0, -1),(3, 1, 2),(-1, 1, 2)]`
Choose the correct alternative:
If A is a non singular matrix of order 3, then |adj (A)| = ______
Find the adjoint of the matrix A = `[(2,3),(1,4)]`
Find the inverse of the following matrix:
`[(3,1),(-1,3)]`
Show that the matrices A = `[(2,2,1),(1,3,1),(1,2,2)]` and B = `[(4/5,(-2)/5,(-1)/5),((-1)/5,3/5,(-1)/5),((-1)/5,(-2)/5,4/5)]` are inverses of each other.
Solve by matrix inversion method:
x – y + 2z = 3; 2x + z = 1; 3x + 2y + z = 4
If A = `[(1,-1),(2,3)]` show that A2 - 4A + 5I2 = 0 and also find A-1.
The matrix M = `[(0,1,2),(1,2,3),(3,1,1)]` and its inverse is N = [nij]. What is the element n23 of matrix N?
If A = `[(4,5),(2,1)]` and A2 - 5A - 6l = 0, then A-1 = ?
If [abc] ≠ 0, then `(["a" + "b b" + "c c" + "a"])/(["b c a"])` = ____________.
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 = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is ______
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
If A = `[(2, 3),(a, 6)]` is a singular matrix, then a = ______.
A–1 exists if |A| = 0.
If matrix P = `[(0, -tan (θ//2)),(tanθ//2, 0)]`, then find (I – P) `[(cosθ, -sinθ),(sinθ, cosθ)]`
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 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.
