Advertisements
Advertisements
प्रश्न
Check whether the following matrices are invertible or not:
`[(3, 4, 3),(1, 1, 0),(1, 4, 5)]`
उत्तर
Let A = `[(3, 4, 3),(1, 1, 0),(1, 4, 5)]`
Then, |A| = `|(3, 4, 3),(1, 1, 0),(1, 4, 5)|`
= 3(5 – 0) – 4(5 – 0) + 3(4 – 1)
= 15 – 20 + 9
= 4 ≠ 0
∴ A is a non-singular matrix.
∴ A is invertible.
APPEARS IN
संबंधित प्रश्न
Find the inverse of the matrix `[(1 2 3),(1 1 5),(2 4 7)]` by adjoint method
Find the inverse of the following matrix by elementary row transformations if it exists.
`A = [(1, 2, -2), (0, -2, 1), (-1, 3, 0)]`
Find the matrix of the co-factor for the following matrix.
`[(1, 0, 2),(-2, 1, 3),(0, 3, -5)]`
Find the inverse of the following matrix by the adjoint method.
`[(1, 0, 0),(3, 3, 0),(5, 2, -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):
`((2,1),(1,-1))`
Choose the correct answer from the given alternatives in the following question:
For a 2 × 2 matrix A, if A(adj A) = `[(10,0),(0,10)]`, then determinant A equals
Choose the correct alternative.
If A2 + mA + nI = O and n ≠ 0, |A| ≠ 0, then A–1 = _______
Fill in the blank :
If A = `[(3, -5),(2, 5)]`, then co-factor of a12 is _______
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, -3, 3),(2, 2, 3),(3, -2, 2)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, 0, -1),(5, 1, 0),(0, 1, 3)]`
Find the inverse of `[(3, 1, 5),(2, 7, 8),(1, 2, 5)]` by adjoint method.
If ω is a complex cube root of unity, then the matrix A = `[(1, ω^2, ω),(ω^2, ω, 1),(ω, 1, ω^2)]` is
A = `[(cos theta, - sin theta),(-sin theta, -cos theta)]` then find A−1
If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A−1 B−1)
Find the inverse of A = `[(sec theta, tan theta, 0),(tan theta, sec theta, 0),(0, 0, 1)]`
The value of Minor of element b22 in matrix B = `[(2, -2),(4, 5)]` is ______
Find the inverse of matrix B = `[(3,1, 5),(2, 7, 8),(1, 2, 5)]` by using adjoint method
Complete the following activity to find inverse of matrix using elementary column transformations and hence verify.
`[(2, 0, -1),(5, 1, 0),(0, 1, 3)]` B−1 = `[(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
C1 → C1 + C3
`[("( )", 0, -1),("( )", 1, 0),("( )", 1, 3)]` B−1 = `[("( )", 0, 0),("( )", 1, 0),("( )", 0, 1)]`
C3 → C3 + C1
`[(1, 0, 0),("( )", 1, "( )"),(3, 1, "( )")]` B−1 = `[(1, 0, "( )"),(0, 1, 0),("( )", 0, "( )")]`
C1 → C1 – 5C2, C3 → C3 – 5C2
`[(1, "( )", 0),(0, 1, 0),("( )", 1, "( )")]` B−1 = `[(1, 0, "( )"),("( )", 1, -5),(1, "( )", 2)]`
C1 → C1 – 2C3, C2 → C2 – C3
`[(1, 0, 0),(0, 1, 0),(0, 0, 1)]` B−1 = `[(3, -1, "( )"),("( )", 6, -5),(5, "( )", "( )")]`
B−1 = `[("( )", "( )", "( )"),("( )", "( )", "( )"),("( )", "( )", "( )")]`
`[(2, "( )", -1),("( )", 1, 0),(0, 1, "( )")] [(3, "( )", "( )"),("( )", 6, "( )"),("( )", -2, "( )")] = [(1, 0, 0),(0, 1, 0),(0, 0, 1)]`
Find the inverse of the following matrix:
`[(-3,-5,4),(-2,3,-1),(1,-4,-6)]`
If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)
If A = `[(-1,2,-2),(4,-3,4),(4,-4,5)]` then, show that the inverse of A is A itself.
Find m if the matrix `[(1,1,3),(2,λ,4),(9,7,11)]` has no inverse.
adj (AB) is equal to:
The inverse matrix of `((3,1),(5,2))` is
If A is an invertible matrix of order 2 then det (A-1) be equal
If A = `|(1,1,1),(3,4,7),(1,-1,1)|` verify that A(adj A) = (adj A)(A) = |A|I3.
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.
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 is non-singular matrix and (A + l)(A - l) = 0 then A + A-1 = ______.
If A = `[(2, -3, 3),(2, 2, 3),(3, "p", 2)]` and A–1 = `[(-2/5, 0, 3/5),(-1/5, 1/5, "q"),(2/5, 1/5, -2/5)]`, then ______.
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 matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A–1 = `1/k` (adj A), then k is ______.
If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A2 – 5A)A–1 = ______.
If A = `[(cos α, sin α),(- sin α, cos α)]`, then the matrix A is ______.
If A = `[(2, 3),(4, 5)]`, show that A2 – 7A – 2I = 0
If A = `[(3, 1),(-1, 2)]`, show that A2 – 5A + 7I = 0
