English

Cosθ[cosθsinθ-sinθcos θ]+sinθ[sinθ-cosθcosθsinθ] = ______ - Mathematics and Statistics

Advertisements
Advertisements

Question

`cos theta [(cos theta, sin theta),(-sin theta, cos  theta)] + sin theta [(sin theta, - cos theta),(cos theta, sin theta)]` = ______

Options

  • `[(0, 0),(0, 0)]`

  • `[(0, 1),(1, 0)]`

  • `[(1, 0),(0, 0)]`

  • `[(1, 0),(0, 1)]`

MCQ
Fill in the Blanks

Solution

`[(1, 0),(0, 1)]`

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.2: Matrics - MCQ

RELATED QUESTIONS

Find the co-factor of the element of the following matrix:

`[(-1, 2),(-3, 4)]`


Find the inverse of `[(1,2,3),(1,1,5),(2,4,7)]` by the adjoint method.


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 `[(1, 2, 3 ),(1, 1, 5),(2, 4, 7)]` of the elementary row tranformation.


If A = `[(1, 0, 1),(0, 2, 3),(1, 2, 1)] "and B" = [(1, 2, 3),(1, 1, 5),(2, 4, 7)]`, then find a matrix X such that XA = B.


If A is a no singular matrix, then det (A–1) = _______


If A = `[(1, 2),(-3, -1)], "B" = [(-1, 0),(1, 5)]`, then AB = 


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.


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 inverse of the following matrices (if they exist) by elementary transformations :

`[(2, -3, 3),(2, 2, 3),(3, -2, 2)]`


Find the inverse of `[(3, 1, 5),(2, 7, 8),(1, 2, 5)]` by adjoint method.


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 A = `[(4, -1),(-1, "k")]` such that A2 − 6A + 7I = 0, then K = ______


If A = `[(2, 4),(1, 3)]` and B = `[(1, 1),(0, 1)]` then find (A−1 B−1)


Find the adjoint of matrix A = `[(2, 0, -1),(3, 1, 2),(-1, 1, 2)]`


If A = [aij]2×2, where aij = i – j, then A = ______


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 – C

`[(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)]`


Find the inverse of the following matrix:

`[(3,1),(-1,3)]`


Show that the matrices A = `[(2,2,1),(1,3,1),(1,2,2)]` and B = `[(4/5,(-2)/5,(-1)/5),((-1)/5,3/5,(-1)/5),((-1)/5,(-2)/5,4/5)]` are inverses of each other.


Find m if the matrix `[(1,1,3),(2,λ,4),(9,7,11)]` has no inverse.


A sales person Ravi has the following record of sales for the month of January, February and March 2009 for three products A, B and C. He has been paid a commission at fixed rate per unit but at varying rates for products A, B and C.

Months Sales in units Commission
A B C
January 9 10 2 800
February 15 5 4 900
March 6 10 3 850

Find the rate of commission payable on A, B and C per unit sold using matrix inversion method.


If A = `((-1,2),(1,-4))` then A(adj A) is


If A = `|(3,-1,1),(-15,6,-5),(5,-2,2)|` then, find the Inverse of A.


If A = `[(1,2),(3,-5)]`, then A-1 = ?


The sum of the cofactors of the elements of second row of the matrix `[(1, 3, 2), (-2, 0, 1), (5, 2, 1)]` is ____________.


If A and Bare square matrices of order 3 such that |A| = 2, |B| = 4, then |A(adj B)| = ______.


If A = `[(1,-1,1),(2,1,-3),(1,1,1)]`, then the sum of the elements of A-1 is ______.


If A = `[(2,  -3, 3),(2, 2, 3),(3, "p", 2)]` and A–1 = `[(-2/5, 0, 3/5),(-1/5, 1/5, "q"),(2/5, 1/5, -2/5)]`, then ______.


Find the cofactors of the elements of the matrix

`[(-1, 2),(-3, 4)]`


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 ______.


The number of solutions of equation x2 – x3 = 1, – x1 + 2x3 = 2, x1 – 2x2 = 3 is ______.


Matrix A = `[(1, 2, 3),(1, 1, 5),(2, 4, 7)]` then the value of a31 A31 + a32 A32 + a33 A33 is ______.


If A = `[(1, 1, 0),(2, 1, 5),(1, 2, 1)]`, then a11A21 + a12A22 + a13A23 is equal to ______.


if `A = [(2,-1,1),(-1,2,-1),(1,-1,2)]` then find A−1 by the adjoint method.


If A = `[(3, 1),(-1, 2)]`, show that A2 – 5A + 7I = 0


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×