हिंदी

State whether the following statement is True or False: If A is non singular, then |A| = 0 - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

State whether the following statement is True or False:

If A is non singular, then |A| = 0

विकल्प

  • True

  • False

MCQ
सत्य या असत्य

उत्तर

False

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

संबंधित प्रश्न

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

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


Determine the product `[(-4,4,4),(-7,1,3),(5,-3,-1)][(1,-1,1),(1,-2,-2),(2,1,3)]` and use it to solve the system of equations x - y + z = 4, x- 2y- 2z = 9, 2x + y + 3z = 1.


If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.


Show that a matrix A = `1/2[(sqrt2,-isqrt2,0),(isqrt2,-sqrt2,0),(0,0,2)]` is unitary.


Identify the following matrix is singular or non-singular?

`[(5, 0, 5),(1, 99, 100),(6, 99, 105)]`


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


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 = `[(6, 0),("p", "q")]` is a scalar matrix, then the values of p and q are ______ respectively.


For the non singular matrix A, (A′)–1 = (A–1)′.


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


If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.

2X + 3Y = `[(2, 3),(4, 0)]`, 3Y + 2Y = `[(-2, 2),(1, -5)]`


The matrix `[(0,-5,8),(5,0,12),(-8,-12,0)]`  is a ____________.


If `[(1,2),(3,4)],` then A2 - 5A is equal to ____________.


If 'A' is square matrix, such that A2 = A, then (7 + A)3 = 7A is equal to


Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the systems of linear equations (A2B2 – B2A2)X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has ______.


If `[(1, 2, 1),(2, 3, 1),(3, a, 1)]` is non-singular matrix and a ∈ A, then the set A is ______.


If A = `[(5, x),(y, 0)]` and A = AT, where AT is the transpose of the matrix A, then ______.


Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A100B = BA100

Reason: AB = BA implies AB = BA for all positive integers n.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×