मराठी

The matrix [100020004] is a ______.

Advertisements
Advertisements

प्रश्न

The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.

पर्याय

  • Identity matrix

  • Symmetric matrix

  • Skew-symmetric matrix

  • None of these

MCQ
रिकाम्या जागा भरा
Advertisements

उत्तर

The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a symmetric matrix.

Explanation:

Let A = `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]`

A' = `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` = A

A' = A

So A is a symmetric matrix.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 3: Matrices - Exercise [पृष्ठ ६०]

APPEARS IN

संबंधित प्रश्‍न

If A is a skew symmetric matric of order 3, then prove that det A  = 0


If A = `[(-1, 2, 3),(5, 7, 9),(-2, 1, 1)]` and B = `[(-4, 1, -5),(1, 2, 0),(1, 3, 1)]`, then verify that (A + B)' = A' + B'


If  A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A + B)' = A' + B'


For the matrices A and B, verify that (AB)′ = B'A', where A = `[(1),(-4),(3)]`, B = `[(-1, 2, 1)]`


Show that the matrix A = `[(1, -1, 5),(-1, 2, 1),(5, 1, 3)]` is a symmetric matrix.


Show that the matrix  A = `[(0, 1, -1),(-1, 0, 1),(1, -1, 0)]` is a skew symmetric matrix.


For the matrix A = `[(1, 5),(6, 7)]`, verify that (A – A') is a skew symmetric matrix.


Find `1/2` (A + A') and `1/2` (A – A'), when A = `[(0, a, b),(-a, 0, c),(-b, -c, 0)]`


Express the following matrices as the sum of a symmetric and a skew symmetric matrix:

`[(1, 5),(-1, 2)]`


Show that the matrix B'AB is symmetric or skew symmetric according as A is symmetric or skew symmetric.


Find the values of x, y, z if the matrix A = `[(0, 2y, z),(x, y, -z),(x, -y, z)]` satisfy the equation A'A = I.


if A =`((5,a),(b,0))` is symmetric matrix show that a = b


If \[A = \begin{bmatrix}1 & 2 \\ 0 & 3\end{bmatrix}\] is written as B + C, where B is a symmetric matrix and C is a skew-symmetric matrix, then B is equal to.


For what value of x, is the matrix \[A = \begin{bmatrix}0 & 1 & - 2 \\ - 1 & 0 & 3 \\ x & - 3 & 0\end{bmatrix}\] a skew-symmetric matrix?


If \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\]  is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is  


If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B is 


If A and B are matrices of the same order, then ABT − BAT is a 


Express the matrix A as the sum of a symmetric and a skew-symmetric matrix, where A = `[(2, 4, -6),(7, 3, 5),(1, -2, 4)]`


Let A = `[(2, 3),(-1, 2)]`. Then show that A2 – 4A + 7I = O. Using this result calculate A5 also.


If A = `[(0, 1),(1, 1)]` and B = `[(0, -1),(1, 0)]`, show that (A + B)(A – B) ≠ A2 – B2 


If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α


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


Sum of two skew-symmetric matrices is always ______ matrix.


If A is a symmetric matrix, then A3 is a ______  matrix.


If A is a skew-symmetric matrix, then A2 is a ______.


If A and B are symmetric matrices, then AB – BA is a ______.


If A and B are symmetric matrices, then BA – 2AB is a ______.


If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.


If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.


The diagonal elements of a skew symmetric matrix are ____________.


If A, B are Symmetric matrices of same order, then AB – BA is a


If A = [aij] is a skew-symmetric matrix of order n, then ______.


If `[(2, 0),(5, 4)]` = P + Q, where P is symmetric, and Q is a skew-symmetric matrix, then Q is equal to ______.


The value of |A|, if A = `[(0, 2x - 1, sqrt(x)),(1 - 2x, 0, 2sqrt(x)),(-sqrt(x), -2sqrt(x), 0)]`, where x ∈ R+, is ______.


For what value of k the matrix `[(0, k),(-6, 0)]` is a skew symmetric matrix?


If A and B are symmetric matrices of the same order, then AB – BA is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×