Advertisements
Advertisements
प्रश्न
Fill in the blank :
If A = [aij]2x3 and B = [bij]mx1 and AB is defined, then m = _______
उत्तर
If A = [aij]2x3 and B = [bij]mx1 and AB is defined, then m = 3.
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]]`
If A = `[(1, 3), (3, 1)]`, Show that A2 - 2A is a scalar matrix.
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 (if they exist):
`((1,-1),(2,3))`
Find the inverse of the following matrix (if they exist):
`[(2,-3,3),(2,2,3),(3,-2,2)]`
Find the inverse of the following matrix (if they exist):
`[(2,0,-1),(5,1,0),(0,1,3)]`
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:
For a 2 × 2 matrix A, if A(adj A) = `[(10,0),(0,10)]`, then determinant A equals
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:
`[(2, 0, −1),(5, 1, 0),(0, 1, 3)]`
Choose the correct alternative.
If AX = B, where A = `[(-1, 2),(2, -1)], "B" = [(1),(1)]`, then X = _______
Fill in the blank :
If A = `[(3, -5),(2, 5)]`, then co-factor of a12 is _______
State whether the following is True or False :
A(adj. A) = |A| I, where I is the unit matrix.
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(1, -1),(2, 3)]`
`cos theta [(cos theta, sin theta),(-sin theta, cos theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______
If A = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then |A| |adj A| = ______
If A = `[(2, 2),(-3, 2)]` and B = `[(0, -1),(1, 0)]`, then find the matrix (B−1 A−1)−1.
If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB
If f(x) = x2 − 2x − 3 then find f(A) when A = `[(1, 2),(2, 1)]`
If A = `[(6, 5),(5, 6)]` and B = `[(11, 0),(0, 11)]` then find A'B'
If A = `[(0, 1),(2, 3),(1, -1)]` and B = `[(1, 2, 1),(2, 1, 0)]`, then find (AB)−1
If A = `[(1, 0, 0),(3, 3, 0),(5, 2, -1)]`, find A−1 by the adjoint method
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 ______
Find the inverse of the following matrix:
`[(1,-1),(2,3)]`
If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)
Solve by matrix inversion method:
2x + 3y – 5 = 0; x – 2y + 1 = 0.
The prices of three commodities A, B, and C are ₹ x, y, and z per unit respectively. P purchases 4 units of C and sells 3 units of A and 5 units of B. Q purchases 3 units of B and sells 2 units of A and 1 unit of C. R purchases 1 unit of A and sells 4 units of B and 6 units of C. In the process P, Q and R earn ₹ 6,000, ₹ 5,000 and ₹ 13,000 respectively. By using the matrix inversion method, find the prices per unit of A, B, and C.
The inverse matrix of `((4/5,(-5)/12),((-2)/5,1/2))` is
If A = `((-1,2),(1,-4))` then A(adj A) is
The matrix A = `[("a",-1,4),(-3,0,1),(-1,1,2)]` is not invertible only if a = _______.
If A = `[(2, -3), (3, 5)]`, then |Adj A| is equal to ______
If A = `[(1, tanx),(-tanx, 1)]`, then AT A–1 = ______.
The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible ______.
If A = `[(1, 2, -1),(-1, 1, 2),(2, -1, 1)]`, then det (adj (adj A)) is ______.
If A = `[(x, 1),(1, 0)]` and A = A–1, then x = ______.
If matrix A = `[(1, 2),(4, 3)]`, such that AX = I, then X is equal to ______.
If A = `[(4, 3, 2),(-1, 2, 0)]`, B = `[(1, 2),(-1, 0),(1, -2)]`
Find (AB)–1 by adjoint method.
Solution:
AB = `[(4, 3, 2),(-1, 2, 0)] [(1, 2),(-1, 0),(1, -2)]`
AB = [ ]
|AB| = `square`
M11 = –2 ∴ A11 = (–1)1+1 . (–2) = –2
M12 = –3 A12 = (–1)1+2 . (–3) = 3
M21 = 4 A21 = (–1)2+1 . (4) = –4
M22 = 3 A22 = (–1)2+2 . (3) = 3
Cofactor Matrix [Aij] = `[(-2, 3),(-4, 3)]`
adj (A) = [ ]
A–1 = `1/|A| . adj(A)`
A–1 = `square`
if `A = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.