Advertisements
Advertisements
प्रश्न
if A =`((5,a),(b,0))` is symmetric matrix show that a = b
Advertisements
उत्तर
A = `((5,a),(b,0))` given A is symmetric matrix
`A = A^T`
`[(5,a),(b,0)] = [(5,a),(b,0)]^T = [(5,b),(a,0)]`
`:. a = b`
APPEARS IN
संबंधित प्रश्न
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' = `[(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 = `[(0),(1),(2)]`, B = `[(1, 5, 7)]`
If A = `[(cos α, sin α), (-sin α, cos α)]`, then verify that A' A = I
For the matrix A = `[(1, 5),(6, 7)]` verify that (A + A') is a symmetric matrix.
If A = [aij] is a square matrix of even order such that aij = i2 − j2, then
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
Let A = `[(2, 3),(-1, 2)]`. Then show that A2 – 4A + 7I = O. Using this result calculate A5 also.
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 ______.
If A and B are symmetric matrices, then AB – BA is a ______.
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
If A and B are any two matrices of the same order, then (AB)′ = A′B′.
If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.
If A is any square matrix, then which of the following is skew-symmetric?
For \[B=\begin{bmatrix}2&-2&-4\\-1&3&4\\1&-2&-3\end{bmatrix}\], what is its symmetric part \[P=\frac{1}{2}(B+B^T)\]?
How many decompositions of a square matrix into a symmetric part and a skew-symmetric part are possible?
