English

If A = [731-2-41591], find (AT)T. - Mathematics and Statistics

Advertisements
Advertisements

Question

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

Sum

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)]` = A.

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Matrices - Exercise 2.2 [Page 46]

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Solve the following equations by reduclion method 

x+3y+3z= 16 ,  x+4y+4z=21 , x+3y+4z = 19 


Solve the following equations by reduction method : 

x + 2y + z = 8 

2x+ 3y - z = 11 

3x - y - 2z = 5


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


For each of the following matrices, find its transpose and state whether it is symmetric, skew-symmetric, or neither.

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


Solve the following equations for X and Y, if 3X − Y = `[(1, -1),(-1, 1)]`  and X – 3Y = `[(0, -1),(0, -1)]`.


If A = `[(1, 2),(-1, -2)], "B" = [(2, "a"),(-1, "b")]` and (A + B)2 = A2 + B2, find the values of a and b.


Find AT,  if A = `[(1, 3),(-4, 5)]`


If [aij]3×3, where aij = 2(i – j), find A and AT. State whether A and AT both are symmetric or skew-symmetric matrices?


If A = `[(1, 2, -5),(2, -3, 4),(-5, 4, 9)]`, prove that AT = A.


If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(2, 1),(4, -1),(-3, 3)], "C" = [(1, 2),(-1, 4),(-2, 3)]`, then show that (A – C)T = AT – CT.


If A = `[(-1, 2, 1),(-3, 2, -3)]` and B = `[(2, 1),(-3, 2),(-1, 3)]`, prove that (A + BT)T = AT + B.


Prove that A + AT is a symmetric and A – AT is a skew symmetric matrix, where A = `[(1, 2, 4),(3, 2, 1),(-2, -3, 2)]`


Prove that A + AT is a symmetric and A – AT is a skew symmetric matrix, where A = `[(5, 2, -4),(3, -7, 2),(4, -5, -3)]`


Express each of the following matrix as the sum of a symmetric and a skew symmetric matrix `[(4, -2),(3, -5)]`.


Express each of the following matrix as the sum of a symmetric and a skew symmetric matrix `[(3, 3, -1),(-2, -2, 1),(-4, -5, 2)]`.


If A = `[(2, -1),(3, -2),(4, 1)] "and B" = [(0, 3, -4),(2, -1, 1)]`, verify that (AB)T = BTAT.


Choose the correct alternative.

The matrix `[(0, 0, 0),(0, 0, 0)]` is _______


Choose the correct alternative.

If A = `[(α, 4),(4, α)]` and |A3| = 729, then α = ______.


Fill in the blank:

A = `[(3),(1)]` is ........................ matrix.


Fill in the blank :

Matrix B = `[(0, 3, 1),(-3, 0, -4),("p", 4, 0)]` is skew symmetric, then the value of p is _______


State whether the following is True or False :

Every scalar matrix is unit matrix.


State whether the following is True or False :

A = `[(4, 5),(6, 1)]` is no singular matrix.


Solve the following :

Find k, if `[(7, 3),(5, "k")]` is a singular matrix.


Solve the following :

Find x, y, z if `[(2, x, 5),(3, 1, z),(y, 5, 8)]` is a symmetric matrix.


If A = `[(2, -3),(5, -4),(-6, 1)], "B" = [(-1, 2),(2, 2), (0, 3)] and "C" = [(4,  3),(-1, 4),(-2, 1)]` Show that A + B = B + A


Simplify, `costheta[(costheta, sintheta),(-sintheta, costheta)] + sintheta[(sintheta, -costheta),(costheta, sintheta)]`


If A = `[("i", 2"i"),(-3, 2)] and "B" = [(2"i", "i"),(2, -3)]`, where `sqrt(-1)` = i,, find A + B and A – B. Show that A + B is a singular. Is A – B a singular ? Justify your answer.


There are two book shops owned by Suresh and Ganesh. Their sales (in Rupees) for books in three subject – Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B.

July sales (in Rupees), Physics Chemistry Mathematics.

A = `[(5600, 6750, 8500),(6650, 7055, 8905)]"First Row Suresh"/"Second Row Ganesh"`

August sales(in Rupees), Physics Chemistry Mathematics

B = `[(6650, 7055, 8905),(7000, 7500, 10200)]"First Row Suresh"/"Second Row Ganesh"` then,

Find the increase in sales in Rupees from July to August 2017.


There are two book shops owned by Suresh and Ganesh. Their sales (in Rupees) for books in three subject – Physics, Chemistry and Mathematics for two months, July and August 2017 are given by two matrices A and B.

July sales (in Rupees), Physics Chemistry Mathematics.

A = `[(5600, 6750, 8500),(6650, 7055, 8905)]"First Row Suresh"/"Second Row Ganesh"`

August sales(in Rupees), Physics Chemistry Mathematics

B = `[(6650, 7055, 8905),(7000, 7500, 10200)]"First Row Suresh"/"Second Row Ganesh"` then,

If both book shops got 10 % profit in the month of August 2017, find the profit for each book seller in each subject in that month


Evaluate : `[2  -1   3][(4),(3),(1)]`


Answer the following question:

Find matrices A and B, where 2A – B = `[(1, -1),(0, 1)]` and A + 3B = `[(1, -1),(0, 1)]`


Choose the correct alternative:

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


Choose the correct alternative:

If A and B are two square matrices of order 3, then (AB)T = ______


State whether the following statement is True or False:

`[(2, 0, 0),(3, -1, 0),(-7, 3, 1)]` is a skew symmetric matrix


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×