Advertisements
Advertisements
प्रश्न
Choose the correct alternative.
If A is a 2 x 2 matrix such that A(adj. A) = `[(5, 0),(0, 5)]`, then |A| = _______
विकल्प
0
5
10
25
उत्तर
5
Explanation:
A(adj A) = |A| I
A(adj A) = `[(5, 0),(0, 5)] = 5[(1, 0),(0, 1)]`
∴ |A| = 5.
APPEARS IN
संबंधित प्रश्न
Find the inverse of the matrix `[(1 2 3),(1 1 5),(2 4 7)]` by adjoint method
If A = `[(1, 3), (3, 1)]`, Show that A2 - 2A is a scalar matrix.
If A = `[(1,-1,2),(3,0,-2),(1,0,3)]` verify that A (adj A) = (adj A) A = | A | I
Find the inverses of the following matrices by the adjoint method:
`[(1,2,3),(0,2,4),(0,0,5)]`
Choose the correct answer from the given alternatives in the following question:
If A = `[("cos"alpha, - "sin"alpha,0),("sin"alpha,"cos"alpha,0),(0,0,1)]` where α ∈ R, then [F(α)]-1 is
Find the inverse of the following matrices by the adjoint method `[(3, -1),(2, -1)]`.
Find the inverse of the following matrices by transformation method:
`[(2, 0, −1),(5, 1, 0),(0, 1, 3)]`
Find the inverse of A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)]` by elementary column transformations.
If A is a no singular matrix, then det (A–1) = _______
Check whether the following matrices are invertible or not:
`[(1, 1),(1, 1)]`
Check whether the following matrices are invertible or not:
`[(1, 2, 3),(2, 4, 5),(2, 4, 6)]`
Find inverse of the following matrices (if they exist) by elementary transformations :
`[(2, 1),(7, 4)]`
Find the inverse of `[(3, 1, 5),(2, 7, 8),(1, 2, 5)]` by adjoint method.
The adjoint matrix of `[(3, -3, 4),(2, -3, 4),(0, -1, 1)]` is ______.
If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB
If A = `[(0, 3, 3),(-3, 0, -4),(-3, 4, 0)]` and B = `[(x),(y),(z)]`, find the matrix B'(AB)
If A is invertible matrix of order 3 and |A| = 5, then find |adj A|
If A = `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`, find adj (A).
State whether the following statement is True or False:
Inverse of `[(2, 0),(0, 3)]` is `[(1/2, 0),(0, 1/3)]`
Find the inverse of the following matrix:
`[(3,1),(-1,3)]`
If A = `[(2,3),(1,-6)]` and B = `[(-1,4),(1,-2)]`, then verify adj (AB) = (adj B)(adj A)
If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.
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 `((3,1),(5,2))` is
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 = `[(0, -1, 0), (1, 0, 0), (0, 0, -1)]`, then A-1 is ______
If A = `[(0, 0, 1), (0, 1, 0), (1, 0, 0)]`, then A-1 = ______
If A = `[(5, -4), (7, -5)]`, then 3A-1 = ______
If A is a solution of x2 - 4x + 3 = 0 and `A=[[2,-1],[-1,2]],` then A-1 equals ______.
If A = `[(-i, 0),(0, i)]`, then ATA is equal to
If A, B are two square matries, such that AB = B, BA = A and n ∈ N then (A + B)n =
Find the cofactors of the elements of the matrix
`[(-1, 2),(-3, 4)]`
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 the inverse of the matrix `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exist, then the value of α is ______.
If A = `[(2, 3),(4, 5)]`, show that A2 – 7A – 2I = 0