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

Find AT, if A = [2-61-405] - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Find AT, if A = `[(2, -6, 1),(-4, 0, 5)]`

बेरीज

उत्तर

A = `[(2, -6, 1),(-4, 0, 5)]`

∴ AT = `[(2, -4),(-6, 0),(1, 5)]`.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 2: Matrices - Exercise 2.4 [पृष्ठ ५९]

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Solve the following equations by reduction method: 

x + y + z = 6,

3x - y + 3z = 10

5x + y - 4z = 3 


Solve the following equations by reduclion method 

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


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

verify that A (adj A) = (adj A) A = |A| . I


Solve the following equations by reduction method : 

x + 2y + z = 8 

2x+ 3y - z = 11 

3x - y - 2z = 5


A computers centre has four expert programmers . The centre needs four application programmes to be developed. The head of the computer centre , after stying carefully the programmes to be developed , estimates the computer time in minutes required by the respective experts to develop the application programmes as follows :

  Programmes
Programmes 1 2 3 4
  (Times in minutes)
A 120 100 80 90
B 80 90 110 70
C 110 140 120 100
D 90 90 80 90

How should the head of the computer centre assign the programmes to the programmers so that the total time required is minimum ? 


If A = `[(1, 2, -3),(-3, 7, -8),(0, -6, 1)], "B" = [(9, -1, 2),(-4, 2, 5),(4, 0, -3)]` then find the matrix C such that A + B + C is a zero matrix.


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


Find a, b, c, if `[(1, 3/5, "a"),("b", -5, -7),(-4, "c", 0)]` is a symmetric matrix.


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.

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


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

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


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


Find x and y, if `[(2x + y, -1, 1),(3, 4y, 4)] [(-1,  6, 4),(3, 0, 3)] = [(3, 5, 5),(6, 18, 7)]`.


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


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


If A = `[(5, 4),(-2, 3)]` and B = `[(-1, 3),(4, -1)]`, then find CT, such that 3A – 2B + C = I, whre I is e unit matrix of order 2.


If A = `[(7, 3, 0),(0, 4, -2)], "B" = [(0, -2, 3),(2, 1, -4)]`, then find 5AT – 5BT.


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)]`.


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


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


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 :

If A and B are square matrices of same order, then (A + B)2 = A2 + 2AB + B2.


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) + C = A + (B + C)


If A = `[(1, -2),(5, 3)], "B" = [(1, -3),(4, -7)]`, then find the matrix A – 2B + 6I, where I is the unit matrix of order 2.


If A = `[(1, 2, -3),(-3, 7, -8),(0, -6, 1)], "B" = [(9, -1, 2),(-4, 2, 5),(4, 0, -3)]` then find the matrix C such that A + B + C is a zero matrix


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.


If = `[(2"a" + "b", 3"a" - "b"),("c" + 2"d", 2"c" - "d")] = [(2, 3),(4, -1)]`, find a, b, c and d.


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


State whether the following statement is True or False:

Every square matrix of order n can be expressed as sum of symmetric and skew symmetric matrix


State whether the following statement is True or False:

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


In a Skew symmetric matrix, all diagonal elements are ______


Find the x, y, z, if `{3[(2,0),(0,2),(2,2)]-4[(1,1),(-1,2),(3,1)]}[(1),(2)]=[(x-3),(y-1),(      2z)]`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×