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

Check whether the following matrices are invertible or not: [1001] - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Check whether the following matrices are invertible or not:

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

बेरीज

उत्तर

Let A = `[(1, 0),(0, 1)]`

Then, |A| = `|(1, 0),(0, 1)|`

= 1 – 0

= 1 ≠ 0

∴ A is a non-singular matrix.

∴ A is invertible.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Matrices - Miscellaneous Exercise 2 [पृष्ठ ८५]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] 12 Standard HSC Maharashtra State Board
पाठ 2 Matrices
Miscellaneous Exercise 2 | Q 4.15 | पृष्ठ ८५

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the inverse of matrix A by using adjoint method; where A = `[(1, 0, 1), (0, 2, 3), (1, 2, 1)]`


If A = `[(1, 3), (3, 1)]`, Show that A2 - 2A is a scalar matrix.


Find the matrix of the co-factor for the following matrix.

`[(1, 0, 2),(-2, 1, 3),(0, 3, -5)]`


Find the inverse of the following matrix by the adjoint method.

`[(-1,5),(-3,2)]`


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 (if they exist):

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


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

`[(2,0,-1),(5,1,0),(0,1,3)]`


Find the inverse of the following matrices by the adjoint method `[(1, 2, 3),(0, 2, 4),(0, 0, 5)]`.


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


Adjoint of `[(2, -3),(4, -6)]` is _______


Choose the correct alternative.

If A2 + mA + nI = O and n ≠ 0, |A| ≠ 0, then A–1 = _______


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


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


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

`[(2, 1),(7, 4)]`


If A = `[(3, 0, 0),(0, 3, 0),(0, 0, 3)]`, then |A| |adj A| = ______


If A = `[(1, -1, 1),(2, 1, -3),(1, 1, 1)]`, 10B = `[(4, 2,2),(-5, 0, ∞),(1, -2, 3)]` and B is the inverse of matrix A, then α = ______


If the inverse of the matrix `[(alpha, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exists then find the value of α


If A is invertible matrix of order 3 and |A| = 5, then find |adj 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 


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.


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


The matrix M = `[(0,1,2),(1,2,3),(3,1,1)]` and its inverse is N = [nij]. What is the element n23 of matrix N?


The matrix A = `[("a",-1,4),(-3,0,1),(-1,1,2)]` is not invertible only if a = _______.


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


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 is non-singular matrix such that (A - 2l)(A - 4l) = 0 then A + 8A-1 = ______.


If A = `[(1 + 2"i", "i"),(- "i", 1 - 2"i")]`, where i = `sqrt-1`, then A(adj A) = ______.


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


If A = `[(5, -4), (7, -5)]`, then 3A-1 =  ______ 


If A–1  = `[(3, -1, 1),(-15, 6, -5),(5, -2, 2)]`, then adj A = ______.


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 the inverse of the matrix `[(α, 14, -1),(2, 3, 1),(6, 2, 3)]` does not exist, then the value of α is ______.


If A = `[(cos α, sin α),(-sin α, cos α)]`, then find α satisfying `0 < α < π/2`, when A + AT = `sqrt(2)  l_2` where AT is transpose of A.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×