English

If A = [731-2-41591], Find (AT)T.

Advertisements
Advertisements

Question

If A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`, Find (AT)T.

Sum
Advertisements

Solution

A = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`

∴ AT = `[(7, -2, 5),(3, -4, 9),(1, 1, 1)]`

∴ (AT)T  = `[(7, 3, 1),(-2, -4, 1),(5, 9, 1)]`.

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Determinants and Matrices - Exercise 4.4 [Page 83]

APPEARS IN

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

 If A is a square matrix such that A2 = I, then find the simplified value of (A – I)3 + (A + I)3 – 7A.


Find the value of x, y, and z from the following equation:

`[(x + y + z), (x + z), (y + z)] = [(9), (5), (7)]`


Find the value of a, b, c and d from the equation:

`[(a - b, 2a + c),(2a - b, 3c + d)] = [(-1, 5),(0, 13)]`


If A is a square matrix such that A2 = A, then (I + A)3 – 7A is equal to ______.


Given `A = [(2,-3),(-4,7)]` compute `A^(-1)` and show that `2A^(-1) = 9I - A`


In a certain city there are 30 colleges. Each college has 15 peons, 6 clerks, 1 typist and 1 section officer. Express the given information as a column matrix. Using scalar multiplication, find the total number of posts of each kind in all the colleges.


If A = `[[0 , 2],[3, -4]]` and kA = `[[0 , 3"a"],[2"b", 24]]` then find the value of k,a and b.


Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

`[(3, -2, 4),(0, 0, -5),(0, 0, 0)]`


Classify the following matrix as, a row, a column, a square, a diagonal, a scalar, a unit, an upper triangular, a lower triangular, a symmetric or a skew-symmetric matrix:

`[(0, 4, 7),(-4, 0, -3),(-7, 3, 0)]`


Identify the following matrix is singular or non-singular?

`[(7, 5),(-4, 7)]`


Find x, y, z If `[(0, -5"i", x),(y, 0, z),(3/2, -sqrt(2), 0)]` is a skew symmetric matrix.


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

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


The following matrix, using its transpose state whether it is symmetric, skew-symmetric, or neither:

`[(0, 1 + 2"i", "i" - 2),(-1 - 2"i", 0, -7),(2 - "i", 7, 0)]`


If A = `[(1, 0),(-1, 7)]`, find k so that A2 – 8A – kI = O, where I is a unit matrix and O is a null matrix of order 2.


Select the correct option from the given alternatives:

If A and B are square matrices of equal order, then which one is correct among the following?


Answer the following question:

If A = `[(1, 2),(3, 2),(-1, 0)]` and B = `[(1, 3, 2),(4, -1, -3)]`, show that AB is singular.


State whether the following statement is True or False:

If A and B are two square matrices such that AB = BA, then (A – B)2 = A2 – 2AB + B2 


If A = `[(3, 1),(-1, 2)]`, then prove that A2 – 5A + 7I = O, where I is unit matrix of order 2


If two matrices A and B are of the same order, then 2A + B = B + 2A.


Show by an example that for A ≠ O, B ≠ O, AB = O


For any square matrix A, AAT is a ____________.


The matrix `[(0,5,-7),(-5,0,11),(7,-11,0)]` is ____________.


If a matrix A is both symmetric and skew symmetric then matrix A is ____________.


If all the elements are zero, then matrix is said to be


Find X, If `[X - 5 - 1] [(1, 0, 2),(0, 2, 1),(2, 0, 3)][(x),(4),(1)] ` = 0


A diagonal matrix in which all diagonal elements are same, is called a ______ matrix.


How many matrices can be obtained by using one or more numbers from four given numbers?


A matrix with only one row is called a:


Which general form represents a row matrix?


What is the order of a row matrix with \[n\] columns?


How is an identity matrix denoted when its order is \[n\]?


Which matrix is an identity matrix?


Which orders can a zero matrix have?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×