Advertisements
Advertisements
प्रश्न
For what value of k the matrix `[(0, k),(-6, 0)]` is a skew symmetric matrix?
Advertisements
उत्तर
Let A = `[(0, k),(-6, 0)]`
∴ AT = `[(0, -6),(k, 0)]`
Given A is a skew-symmetric matrix.
∴ AT = – A
`[(0, -6),(k, 0)] = -[(0, k),(-6, 0)]`
= `[(0, -k),(6, 0)]`
On equating the corresponding entries,
k = 6
APPEARS IN
संबंधित प्रश्न
If A' = `[(-2, 3),(1, 2)]` and B = `[(-1, 0),(1, 2)]`, then find (A + 2B)'
If A = `[(sin α, cos α), (-cos α, sin 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 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 matrix A is both symmetric and skew-symmetric, then
The matrix \[\begin{bmatrix}0 & 5 & - 7 \\ - 5 & 0 & 11 \\ 7 & - 11 & 0\end{bmatrix}\] is
Let A = `[(2, 3),(-1, 2)]`. Then show that A2 – 4A + 7I = O. Using this result calculate A5 also.
Show that A′A and AA′ are both symmetric matrices for any matrix A.
If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A′BA is skew-symmetric.
Sum of two skew-symmetric matrices is always ______ matrix.
If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.
If A and B are symmetric matrices of the same order, then ____________.
If A is any square matrix, then which of the following is skew-symmetric?
If A, B are Symmetric matrices of same order, then AB – BA is a
Let A and B be and two 3 × 3 matrices. If A is symmetric and B is skewsymmetric, then the matrix AB – BA is ______.
Which of the following is correct?
Why does multiplying \[A+A^T\] by \[\frac{1}{2}\] not change its symmetric property?
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?
