Advertisements
Advertisements
प्रश्न
State whether the following is True or False :
If A and B are conformable for the product AB, then (AB)T = ATBT.
पर्याय
True
False
उत्तर
(AB)T = BTAT False.
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 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,-1,2),(-2,3,5),(-2,0,-1)]`
Find the inverse of the following matrix by the adjoint method.
`[(2,-2),(4,3)]`
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.
`[(0,1,2),(1,2,3),(3,1,1)]`
Find the inverse of the following matrix.
`[(2,0,-1),(5,1,0),(0,1,3)]`
Find the inverse of the following matrix (if they exist):
`[(2,-3),(5,7)]`
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 = `[("cos"alpha,-"sin"alpha),("sin"alpha,"cos"alpha)]`, then A-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
State whether the following is True or False :
A = `[(2, 1),(10, 5)]` is invertible matrix.
Solve the following :
If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (3A – 5BT)T = 3AT – 5B.
Check whether the following matrices are invertible or not:
`[(1, 2, 3),(2, 4, 5),(2, 4, 6)]`
The solution (x, y, z) of the equation `[(1, 0, 1),(-1, 1, 0),(0, -1, 1)] [(x),(y),(z)] = [(1),(1),(2)]` is (x, y, z) =
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
If A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______
If A = `[(0, 0, -1),(0, -1, 0),(-1, 0, 0)]`, then the only correct statement about the matrix A is ______
If A = `[(4, 5),(2, 5)]`, then |(2A)−1| = ______
If `[(x - y - z),(-y + z),(z)] = [(0),(5),(3)]`, then the value of x, y and z are respectively ______
If the inverse of the matrix `[(alpha, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exists then find the value of α
A + I = `[(3, -2),(4, 1)]` then find the value of (A + I)(A − I)
Find the adjoint of matrix A = `[(6, 5),(3, 4)]`
The sum of three numbers is 20. If we multiply the first by 2 and add the second number and subtract the third we get 23. If we multiply the first by 3 and add second and third to it, we get 46. By using the matrix inversion method find the numbers.
Weekly expenditure in an office for three weeks is given as follows. Assuming that the salary in all the three weeks of different categories of staff did not vary, calculate the salary for each type of staff, using the matrix inversion method.
Week | Number of employees | Total weekly salary (in ₹) |
||
A | B | C | ||
1st week | 4 | 2 | 3 | 4900 |
2nd week | 3 | 3 | 2 | 4500 |
3rd week | 4 | 3 | 4 | 5800 |
If A = `|(1,1,1),(3,4,7),(1,-1,1)|` verify that A(adj A) = (adj A)(A) = |A|I3.
If A = `[(4,5),(2,1)]` and A2 - 5A - 6l = 0, then A-1 = ?
If [abc] ≠ 0, then `(["a" + "b b" + "c c" + "a"])/(["b c a"])` = ____________.
If a 3 × 3 matrix A has its inverse equal to A, then A2 = ______
If A = `[(1,-1,1),(2,1,-3),(1,1,1)]`, then the sum of the elements of A-1 is ______.
If matrix A = `[(1, -1),(2, 3)]` such that AX = I, then X is equal to ______.
If A, B are two square matries, such that AB = B, BA = A and n ∈ N then (A + B)n =
The number of solutions of equation x2 – x3 = 1, – x1 + 2x3 = 2, x1 – 2x2 = 3 is ______.
If A = `[(x, 1),(1, 0)]` and A = A–1, then x = ______.
If the inverse of the matrix `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exist, then the value of α is ______.
For an invertible matrix A, if A (adj A) = `|(20, 0),(0, 20)|`, then | A | = ______.
if `A = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.
If A = `[(2, 3),(4, 5)]`, show that A2 – 7A – 2I = 0