Advertisements
Advertisements
प्रश्न
If A = `[(1, -1, 1),(2, 1, -3),(1, 1, 1)]`, 10B = `[(4, 2,2),(-5, 0, ∞),(1, -2, 3)]` and B is the inverse of matrix A, then α = ______
पर्याय
–2
–1
2
5
उत्तर
5
APPEARS IN
संबंधित प्रश्न
Find the inverse of matrix A by using adjoint method; where A = `[(1, 0, 1), (0, 2, 3), (1, 2, 1)]`
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 co-factor of the element of the following matrix:
`[(-1, 2),(-3, 4)]`
Find the inverse of the following matrix.
`[(0,1,2),(1,2,3),(3,1,1)]`
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
Choose the correct answer from the given alternatives in the following question:
The inverse of a symmetric matrix is
Find the inverse of the following matrices by the adjoint method `[(1, 2, 3),(0, 2, 4),(0, 0, 5)]`.
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 :
`[(2, 1),(7, 4)]`
For an invertible matrix A, if A . (adj A) = `[(10, 0),(0, 10)]`, then find the value of |A|.
If A = `[("a", "b"),("c", "d")]` then find the value of |A|−1
If A = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)]` and B = `[(x),(y),(z)]`, find the matrix B'(AB)
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)]`
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
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 adjoint of the matrix A = `[(2,3),(1,4)]`
If A = `[(-1,2,-2),(4,-3,4),(4,-4,5)]` then, show that the inverse of A is A itself.
Solve by matrix inversion method:
3x – y + 2z = 13; 2x + y – z = 3; x + 3y – 5z = - 8
Which of the following matrix has no inverse
If A = `((-1,2),(1,-4))` then A(adj A) is
If A = `|(1,1,1),(3,4,7),(1,-1,1)|` verify that A(adj A) = (adj A)(A) = |A|I3.
If A = `[(1,-1),(2,3)]` show that A2 - 4A + 5I2 = 0 and also find A-1.
Solve by using matrix inversion method:
x - y + z = 2, 2x - y = 0, 2y - z = 1
If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, then B-1A-1 = ?
If A = `[(4,5),(2,1)]` and A2 - 5A - 6l = 0, then A-1 = ?
If A is non-singular matrix and (A + l)(A - l) = 0 then A + A-1 = ______.
If A = `[(1 + 2"i", "i"),(- "i", 1 - 2"i")]`, where i = `sqrt-1`, then A(adj A) = ______.
If ω is a complex cube root of unity and A = `[(ω,0,0),(0,ω^2,0),(0,0,1)]` then A-1 = ?
If A = `[(2, -3), (3, 5)]`, then |Adj A| is equal to ______
If A = `[(1,-1,1),(2,1,-3),(1,1,1)]`, then the sum of the elements of A-1 is ______.
If A is a solution of x2 - 4x + 3 = 0 and `A=[[2,-1],[-1,2]],` then A-1 equals ______.
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, B are two square matries, such that AB = B, BA = A and n ∈ N then (A + B)n =
If A = `[(2, 3),(a, 6)]` is a singular matrix, then a = ______.
Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.
If A = `[(1, 2, 4),(4, 3, -2),(1, 0, -3)]`. Show that A–1 exists and find A–1 using column transformation.
If A = `[(3, 1),(-1, 2)]`, show that A2 – 5A + 7I = 0