English

Apply the given elementary transformation of the following matrix. Use suitable transformation on [1234] to convert it into an upper triangular matrix. - Mathematics and Statistics

Advertisements
Advertisements

Question

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.

Sum
Advertisements

Solution

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

By R2 − 3R1, we get,

A ∼ `[(1,2),(0,-2)]`

This is an upper triangular matrix.

shaalaa.com
Elementry Transformations
  Is there an error in this question or solution?
Chapter 2: Matrics - Exercise 2.1 [Page 39]

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.

A = `[(1,2,-1),(0,1,3)]`, 2C2

B = `[(1,0,2),(2,4,5)]`, −3R1

Find the addition of the two new matrices.


Apply the given elementary transformation of the following matrix.

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


Apply the given elementary transformation of the following matrix.

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

and A = `[(1,-1,3),(2,1,0),(3,3,1)]`, C3 + 2C2 and then 3R3
What do you conclude?


Apply the given elementary transformation of the following matrix.

Transform `[(1,-1,2),(2,1,3),(3,2,4)]` into an upper triangular matrix by suitable column transformations.


Check whether the following matrix is invertible or not:

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


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:

`[(3,4,3),(1,1,0),(1,4,5)]`


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.


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


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


Find the matrix X such that AX = B, where A = `[(1,2),(-1,3)]` and B = `[(0,1),(2,4)]`


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


If A = `[(1,1),(1,2)], "B" = [(4,1),(3,1)]` and C = `[(24,7),(31,9)]`, then find the matrix X such that AXB = C


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` 


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.


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:

The inverse of `[(0,1),(1,0)]` is


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, 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)]`


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


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 = `[(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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×