Advertisements
Advertisements
प्रश्न
Fill in the blank :
If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = _______
उत्तर
If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = – 1.
APPEARS IN
संबंधित प्रश्न
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 inverse of the matrix `[(1 2 3),(1 1 5),(2 4 7)]` by adjoint method
Find the adjoint of the following matrix.
`[(2,-3),(3,5)]`
Find the inverse of the following matrix by the adjoint method.
`[(2,-2),(4,3)]`
Find the inverse of the following matrix.
`[(2, -3),(-1, 2)]`
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 = `[(1,2),(3,4)]`, and A (adj A) = kI, then the value of k is
Choose the correct answer from the given alternatives in the following question:
If A = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`, then A-1 = _____
Choose the correct answer from the given alternatives in the following question:
If A−1 = `- 1/2[(1,-4),(-1,2)]`, then A = ______.
Find the inverse `[(1, 2, 3 ),(1, 1, 5),(2, 4, 7)]` of the elementary row tranformation.
Choose the correct alternative.
If AX = B, where A = `[(-1, 2),(2, -1)], "B" = [(1),(1)]`, then X = _______
Choose the correct alternative.
If a 3 x 3 matrix B has it inverse equal to B, thenB2 = _______
State whether the following is True or False :
If A and B are conformable for the product AB, then (AB)T = ATBT.
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, -3, 3),(2, 2, 3),(3, -2, 2)]`
If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB
Find the adjoint of matrix A = `[(2, 0, -1),(3, 1, 2),(-1, 1, 2)]`
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
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)]`
If A = `[(a,b),(c,d)]` such that ad - bc ≠ 0 then A-1 is
If A is 3 × 3 matrix and |A| = 4 then |A-1| is equal to:
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
If A = `[(4,5),(2,1)]` and A2 - 5A - 6l = 0, then A-1 = ?
If A = `[(3, -3, 4), (2, -3, 4), (0, -1, 1)]` then A-1 = ______
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
If A = `[(0, 0, 1), (0, 1, 0), (1, 0, 0)]`, then A-1 = ______
The inverse of `[(1,cos alpha),(- cos alpha, -1)]` is ______.
If A is a solution of x2 - 4x + 3 = 0 and `A=[[2,-1],[-1,2]],` then A-1 equals ______.
If A = `[(cos theta, sin theta, 0),(-sintheta, costheta, 0),(0, 0, 1)]`, where A11, A11, A13 are co-factors of a11, a12, a13 respectively, then the value of a11A11 + a12A12 + a13A13 = ______.
If matrix A = `[(1, -1),(2, 3)]` such that AX = I, then X is equal to ______.
If matrix P = `[(0, -tan (θ//2)),(tanθ//2, 0)]`, then find (I – P) `[(cosθ, -sinθ),(sinθ, cosθ)]`
If matrix A = `[(3, -2, 4),(1, 2, -1),(0, 1, 1)]` and A–1 = `1/k` (adj A), then k is ______.
If A = `[(0, 0, 1),(0, 1, 0),(1, 0, 0)]`, then A2008 is equal to ______.
If A = `[(1, 2, 3),(-1, 1, 2),(1, 2, 4)]` then (A2 – 5A)A–1 = ______.
The inverse of the matrix `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]` is ______.
If matrix A = `[(1, -1),(2, 3)]`, then A2 – 4A + 5I is where I is a unit matix.
If A = `[(1, 2, 4),(4, 3, -2),(1, 0, -3)]`. Show that A–1 exists and find A–1 using column transformation.
