English

Check whether the following matrix is invertible or not: [1001] - Mathematics and Statistics

Advertisements
Advertisements

Question

Check whether the following matrix is invertible or not:

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

Sum

Solution

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

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

∴ A is a non-singular matrix.

Hence, A-1 exists.

shaalaa.com
Elementry Transformations
  Is there an error in this question or solution?
Chapter 2: Matrics - Miscellaneous exercise 2 (A) [Page 52]

APPEARS IN

RELATED QUESTIONS

Apply the given elementary transformation of the following matrix.

A = `[(1,0),(-1,3)]`, R1↔ R2


Apply the given elementary transformation of the following matrix.

B = `[(1, -1, 3),(2, 5, 4)]`, R1→ R1 – R2


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?


Apply the given elementary transformation of the following matrix.

Use suitable transformation on `[(1,2),(3,4)]` to convert it into an upper triangular matrix.


Apply the given elementary transformation of the following matrix.

Convert `[(1,-1),(2,3)]` into an identity matrix by suitable row transformations.


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


Check whether the following matrix is invertible or not:

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


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:

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


If A = `[(1,2),(3,4)]` and X is a 2 × 2 matrix such that AX = I, find X.


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


If A = `[(2,3),(1,2)]`, B = `[(1,0),(3,1)]`, find AB and (AB)-1 . Verify that (AB)-1 = B-1.A-1.


If A = `[(4,5),(2,1)]`, show that `"A"^-1 = 1/6("A" - 5"I")`.


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


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

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


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

If A = `[(1,2),(3,4)]` , adj A = `[(4,"a"),(-3,"b")]`, then the values of a and b are


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


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


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


Find the matrix X such that AX = I where A = `[(6, 17),(1, 3)]`


Find A−1 using column transformations:

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


Find A−1 using column transformations:

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


If A = `[(1, 2, -1),(3, -2, 5)]`, apply R1 ↔ R2 and then C1 → C1 + 2C3 on A


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


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


If A = `[(3, -1),(4, 2)]`, B = `[(2),(-1)]`, find X such that AX = B.


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


Find the matrix X such that AX = B, where A = `[(2, 1),(-1, 3)]`, B = `[(12, -1),(1, 4)]`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×