मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

State whether the following is True or False : If A and B are conformable for the product AB, then (AB)T = ATBT. - Mathematics and Statistics

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

MCQ
चूक किंवा बरोबर

उत्तर

(AB)T = BTAT False.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Matrices - Miscellaneous Exercise 2 [पृष्ठ ८३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
पाठ 2 Matrices
Miscellaneous Exercise 2 | Q 3.07 | पृष्ठ ८३

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×