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

State whether the following statement is True or False: [2003-10-731] is a skew symmetric matrix - Mathematics and Statistics

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प्रश्न

State whether the following statement is True or False:

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

पर्याय

  • True

  • False

MCQ
चूक किंवा बरोबर

उत्तर

False

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1.2: Matrices - Q.2

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्‍न

Find the values of x and y if

`2 [(x,5),(7,y-3)] [(3,-4),(1,2)] = [(7,6),(15,14)]`


Solve the following equations by reduction method: 

x + y + z = 6,

3x - y + 3z = 10

5x + y - 4z = 3 


Solve the following equations by reduction method: 

x+ y+z = 6,

3x-y+3z = 10

5x+ y-4z = 3 


Find x , y , z , w if `[("x+y","x-y"),("y+z+w","2w-z")]` = `[(2,-1),(9,5)]`


Simplify the following :

`{3 [(1,2,0),(0,-1,3)] - [(1,5,-2),(-3,-4,4)]} [(1),(2),(1)]`


If A = `[(1,2,3),(2,"a",2),(5,7,3)]` is a singular matrix , find the value of 'a'.


Find x and y if `x + y = [(7,0),(2,5)] , x - y[(3,0),(0,3)]`


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


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)]`


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


Find AT,  if A = `[(1, 3),(-4, 5)]`


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


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)]`


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 :

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


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.


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

If A = `[(2, 1),(0, 3)]`, B = `[(1, 2),(3, -2)]`, verify that |AB| = |A||B|


Choose the correct alternative:

If A = `[(1, 3/5, x),(y, -5, -7),(-4, -7, 0)]` is a symmetric matrix, then the values of x and y are ______ respectively.


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 = ______


In a Skew symmetric matrix, all diagonal elements are ______


If A = `[(2, 5),(1, 3)]` then A–1 = ______.


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