हिंदी

State whether the following statement is True or False: If A = [12-52-34-549], then AT = A - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

State whether the following statement is True or False:

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

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

True

shaalaa.com
Properties of Matrices
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.2: Matrices - Q.2

संबंधित प्रश्न

Evaluate : `[(3),(2),(1)][2  -4   3]`


Evaluate : `[2 - 1   3][(4),(3),(1)]`


Verify that A(B + C) = AB + AC, if A = `[(4, -2),(2, 3)], "B" = [(-1, 1),(3, -2)] " and C" = [(4 ,1),(2, -1)]`.


If A = `[(1, 2, 2),(2, 1, 2),(2, 2, 1)]`, show that A2 – 4A is a scalar matrix.


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


If A = `[(3, 1),(-1, 2)]`, prove that A2 – 5A + 7I = 0, where I is a 2 x 2 unit matrix.


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


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


Jay and Ram are two friends. Jay wants to buy 4 pens and 8 notebooks, Ram wants to buy 5 pens and 12 notebooks. The price of one pen and one notebook was ₹ 6 and ₹ 10 respectively. Using matrix multiplication, find the amount each one of them requires for buying the pens and notebooks.


Choose the correct alternative.

If A and B are square matrices of order n × n such that A2 – B2 = (A – B)(A + B), then which of the following will be always true?


Solve the following :

If A = `[(2, -3),(3, -2),(-1, 4)],"B" = [(-3, 4, 1),(2, -1, -3)]`, verify (A + 2BT)T = AT + 2B.


Solve the following :

If A = `[(3, 1),(1, 5)], "B" = [(1, 2),(5, -2)]`, verify |AB| = |A| |B|.


Solve the following :

If A = `[(2, -1),(-1, 2)]`, then show that A2 – 4A + 3I = 0.


Solve the following :

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


If matrix form of given equations 3x – y = 1 and y + 4x = 6 is AX = B, then A = ______


If A = `[(2, 1),(0, 3),(1, -1)]` and B = `[(0, 3, 5),(1, -7, 2)]`, then verify (BA)T = ATBT


If A = `[(3, 1),(1, 5)]` and B = `[(1, 2),(5, -2)]`, then verify |AB| = |A||B|


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×