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

Check whether the following matrices are invertible or not: [123245246] - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Check whether the following matrices are invertible or not:

`[(1, 2, 3),(2, 4, 5),(2, 4, 6)]`

बेरीज

उत्तर

Let A = `[(1, 2, 3),(2, 4, 5),(2, 4, 6)]`

Then, |A| = `|(1, 2, 3),(2, 4, 5),(2, 4, 6)|`
= 1(24 – 20) – 2(12 – 10) + 3(8 – 8)
= 4 –  4 + 0
= 0
∴ A is a singular matrix.
∴ A is not 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)]`


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.

`[(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):

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


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

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


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

The inverse of a symmetric matrix is


Find the inverse of the following matrices by the adjoint method `[(3, -1),(2, -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 = 


Fill in the blank :

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


Fill in the blank :

If A = `[(2, 1),(1, 1)] "and" "A"^-1 = [(1, 1),(x, 2)]`, then x = _______


Check whether the following matrices are invertible or not:

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


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


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


Find the inverse of A = `[(sec theta, tan theta, 0),(tan theta, sec theta, 0),(0, 0, 1)]`


Choose the correct alternative:

If A is a non singular matrix of order 3, then |adj (A)| =  ______


Find the inverse of matrix B = `[(3,1, 5),(2, 7, 8),(1, 2, 5)]` by using adjoint method


If A = `[(2,-2,2),(2,3,0),(9,1,5)]` then, show that (adj A) A = O.


The inverse matrix of `((3,1),(5,2))` 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:


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 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), (3, 5)]`, then |Adj A| is equal to ______ 


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


The matrix `[(lambda, 1, 0),(0, 3, 5),(0, -3, lambda)]` is invertible ______.


The inverse of the matrix A = `[(3, 0, 0),(0, 4, 0),(0, 0, 5)]` is ______.


A–1 exists if |A| = 0.


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 ______.


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 matrix A = `[(1, 2),(4, 3)]`, such that AX = I, then X is equal to ______.


If A = `[(1, 2),(3, 4)]` verify that A (adj A) = (adj A) A = |A| I


Find the inverse of the matrix `[(1, 1, 1),(1, 2, 3),(3, 2, 2)]` by elementary column transformation.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×