हिंदी

State whether the following is True or False : A = [21105] is invertible matrix. - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

State whether the following is True or False :

A = `[(2, 1),(10, 5)]` is invertible matrix.

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

A = `|(2, 1),(10, 5)|` 
= 10 – 10
= 0
False.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 2: Matrices - Miscellaneous Exercise 2 [पृष्ठ ८३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
अध्याय 2 Matrices
Miscellaneous Exercise 2 | Q 3.09 | पृष्ठ ८३

वीडियो 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 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.

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


Find AB, if A = `((1,2,3),(1,-2,-3))` and B = `((1,-1),(1,2),(1,-2))`. Examine whether AB has inverse or not.


Find the inverse of the following matrix (if they exist):

`[(2,-3),(5,7)]`


Find the inverse of the following matrices by the adjoint method `[(2, -2),(4, 5)]`.


Fill in the blank :

If A = [aij]mxm is a non-singular matrix, then A–1 = `(1)/(......)` adj(A).


Check whether the following matrices are invertible or not:

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


A = `[(cos alpha, - sin alpha,  0),(sin alpha, cos alpha,  0),(0, 0, 1)]`, then A−1 is


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 = `[("a", "b"),("c", "d")]` then find the value of |A|−1 


If A(α) = `[(cos alpha, sin alpha),(-sin alpha, cos alpha)]` then prove that A2(α) = A(2α)


If A = `[(1, 2),(3, -2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, 3)]` then find the order of AB


If A = `[(-1),(2),(3)]`, B = `[(3, 1, -2)]`, find B'A'


Find the adjoint of matrix A = `[(6, 5),(3, 4)]`


If A = `[(0, 4, 3),(1, -3, -3),(-1, 4, 4)]`, then find A2 and hence find A−1 


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


If A = `[(-4, -3, -3),(1, 0, 1),(4, 4, 3)]`, find adj (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)]`


If A-1 = `[(1,0,3),(2,1,-1),(1,-1,1)]`  then, find A.


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 `((4/5,(-5)/12),((-2)/5,1/2))` is


If A is an invertible matrix of order 2 then det (A-1) be equal


If A is 3 × 3 matrix and |A| = 4 then |A-1| is equal to:


The cost of 2 Kg of Wheat and 1 Kg of Sugar is ₹ 70. The cost of 1 Kg of Wheat and 1 Kg of Rice is ₹ 70. The cost of 3 Kg of Wheat, 2 Kg of Sugar and 1 Kg of rice is ₹ 170. Find the cost of per kg each item using the matrix inversion method.


If A = `[(4,5),(2,1)]` and A2 - 5A - 6l = 0, 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 [abc] ≠ 0, then `(["a" + "b b" + "c c" + "a"])/(["b c a"])` = ____________.


If A = `[(3, -3, 4), (2, -3, 4), (0, -1, 1)]` then A-1 = ______


If A = `[(0, 0, 1), (0, 1, 0), (1, 0, 0)]`, then A-1 = ______ 


If A is a solution of x2 - 4x + 3 = 0 and `A=[[2,-1],[-1,2]],` then A-1 equals ______.


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 ______.


If A = `[(-i, 0),(0, i)]`, then ATA is equal to


If A = `[(2, 3),(a, 6)]` is a singular matrix, then a = ______.


If A = `[(x, 1),(1, 0)]` and A = A–1, then x = ______.


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


For an invertible matrix A, if A (adj A) = `|(20, 0),(0, 20)|`, then | A | = ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×