Advertisements
Advertisements
प्रश्न
The matrix \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is
विकल्प
identity matrix
symmetric matrix
skew-symmetric matrix
diagonal matrix
Advertisements
उत्तर
Given:
\[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\]
\[A^T = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}^T \]
\[ = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\]
\[ = A\]
APPEARS IN
संबंधित प्रश्न
Matrix A = `[(0,2b,-2),(3,1,3),(3a,3,-1)]`is given to be symmetric, find values of a and b
If A= `((3,5),(7,9))`is written as A = P + Q, where P is a symmetric matrix and Q is skew symmetric matrix, then write the matrix P.
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 = `[(cos α, sin α), (-sin α, cos α)]`, then verify that A' A = I
Show that the matrix A = `[(1, -1, 5),(-1, 2, 1),(5, 1, 3)]` is a symmetric matrix.
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(3, 5),(1, -1)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(1, 5),(-1, 2)]`
If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.
If the matrix A is both symmetric and skew symmetric, then ______.
If A is a square matrix, then AA is a
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 = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α
If the matrix `[(0, "a", 3),(2, "b", -1),("c", 1, 0)]`, is a skew symmetric matrix, find the values of a, b and c.
If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew-symmetric.
The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.
If A and B are matrices of same order, then (AB′ – BA′) is a ______.
______ matrix is both symmetric and skew-symmetric matrix.
If A is a symmetric matrix, then A3 is a ______ matrix.
If A is skew-symmetric, then kA is a ______. (k is any scalar)
If A and B are symmetric matrices, then BA – 2AB is a ______.
If A is symmetric matrix, then B′AB is ______.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.
AA′ is always a symmetric matrix for any matrix A.
If A is skew-symmetric matrix, then A2 is a symmetric matrix.
If ax4 + bx3 + cx2 + dx + e = `|(2x, x - 1, x + 1),(x + 1, x^2 - x, x - 1),(x - 1, x + 1, 3x)|`, then the value of e is ______.
Let A and B be and two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is ______.
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 ______.
A square matrix \[A=[a_{ij}]_{n\times n}\] is symmetric when which condition holds?
For a symmetric matrix \[A=[a_{ij}]_{n\times n}\], which entrywise relation is true for all \[i\] and \[j\]?
A square matrix \[A=[a_{ij}]_{n\times n}\] is skew-symmetric when which condition holds?
For a skew-symmetric matrix \[A=[a_{ij}]_{n\times n}\], which relation holds for all \[i\] and \[j\]?
Which identity is used to replace \[(A^T)^T\] by \[A\] when proving that \[A+A^T\] is symmetric?
Which expression writes any square matrix \[A\] as the sum of a symmetric and a skew-symmetric matrix?
