हिंदी

Apply the given elementary transformation of the following matrix. A = [5413], C1↔ C2; B = [3145] R1↔ R2. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Apply the given elementary transformation of the following matrix.

A = `[(5,4),(1,3)]`, C1↔ C2; B = `[(3,1),(4,5)]` R1↔ R2.
What do you observe?

योग

उत्तर

A = `[(5,4),(1,3)]`

By C1↔ C2, we get,

A ∼ `[(4,5),(3,1)]` ...........(1)

B = `[(3,1),(4,5)]`

By R1↔ R2, we get,

B ∼ `[(4,5),(3,1)]` .........(2)

From (1) and (2), we observe that the new matrices are equal.

shaalaa.com
Elementry Transformations
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Matrics - Exercise 2.1 [पृष्ठ ३९]

संबंधित प्रश्न

Apply the given elementary transformation of the following matrix.

A = `[(1,-1,3),(2,1,0),(3,3,1)]`, 3R3 and then C3 + 2C2


The total cost of 3 T.V. sets and 2 V.C.R.’s is ₹ 35,000. The shopkeeper wants a profit of ₹ 1000 per T.V. set and ₹ 500 per V.C.R. He sells 2 T.V. sets and 1 V.C.R. and gets the total revenue as ₹ 21,500. Find the cost price and the selling price of a T.V. set and a V.C.R.


If A = `[(2,1,3),(1,0,1),(1,1,1)]`, then reduce it to I3 by using row transformations.


Check whether the following matrix is invertible or not:

`((1,1),(1,1))`


Check whether the following matrix is invertible or not:

`((1,2),(3,3))`


Check whether the following matrix is invertible or not:

`((2,3),(10,15))`


Check whether the following matrix is invertible or not:

`[(cos theta, sin theta),(-sin theta, cos theta)]`


Check whether the following matrix is invertible or not:

`(("sec" theta , "tan" theta),("tan" theta,"sec" theta))`


Check whether the following matrix is invertible or not:

`((1,2,3),(3,4,5),(4,6,8))`


If A = `[("x",0,0),(0,"y",0),(0,0,"z")]` is a non-singular matrix, then find A−1 by using elementary row transformations. Hence, find the inverse of `[(2,0,0),(0,1,0),(0,0,-1)]`


Find the inverse of A = `[("cos" theta, -"sin" theta, 0),("sin" theta, "cos" theta, 0),(0,0,1)]` by elementary column transformations.


Find X, if AX = B, where A = `[(1,2,3),(-1,1,2),(1,2,4)]` and B = `[(1),(2),(3)]`


Find A-1 by the adjoint method and by elementary transformations, if A = `[(1,2,3),(-1,1,2),(1,2,4)]`


Find the inverse of A = `[(1,0,1),(0,2,3),(1,2,1)]` by using elementary column transformations.


Find the inverse of `[(1,2,3),(1,1,5),(2,4,7)]` by using elementary row transformations.


Show with the usual notation that for any matrix A = `["a"_"ij"]_(3xx3)  "is"   "a"_11"A"_21 + "a"_12"A"_22 + "a"_13"A"_23 = 0` 


Show with the usual notation that for any matrix A = `["a"_"ij"]_(3xx3)  "is"   "a"_11"A"_11 + "a"_12"A"_12 + "a"_13"A"_13 = |"A"|` 


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.


Choose the correct answer from the given alternatives in the following question:

If A = `[(1,2),(2,1)]` and A(adj A) = k I, then the value of k is


The element of second row and third column in the inverse of `[(1, 2, 1),(2, 1, 0),(-1, 0, 1)]` is ______.


If A = `[(2, -1, 1),(-2, 3, -2),(-4, 4, -3)]` the find A2 


If A = `[(-2, 4),(-1, 2)]` then find A2 


Find A−1 using column transformations:

A = `[(5, 3),(3, -2)]`


Find A−1 using column transformations:

A = `[(2, -3),(-1, 2)]`


Find the matrix X such that `[(1, 2, 3),(2, 3, 2),(1, 2, 2)]` X = `[(2, 2, -5),(-2, -1, 4),(1, 0, -1)]`


Find the inverse of A = `[(2, -3, 3),(2, 2, 3),(3, -2, 2)]` by using elementary row transformations.


If A = `[(cosθ, -sinθ, 0),(sinθ, cosθ, 0),(0, 0, 1)]`, find A–1


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×