Which one of the following statements is corr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $A$ be a skew-symmetric matrix of order $n 	imes n$. By definition,$A^T = -A$. Taking the determinant on both sides,we have $\det(A^T) = \det

Vedclass · Accepted Answer

Skew-symmetric matrix of odd order is singular

Vedclass · Answer

(B) Let $A$ be a skew-symmetric matrix of order $n 	imes n$. By definition,$A^T = -A$. Taking the determinant on both sides,we have $\det(A^T) = \det(-A)$. Since $\det(A^T) = \det(A)$ and $\det(-A) = (-1)^n \det(A)$,we get $\det(A) = (-1)^n \det(A)$. If $n$ is odd,then $(-1)^n = -1$,so $\det(A) = -\det(A)$,which implies $2 \det(A) = 0$,or $\det(A) = 0$. $A$ matrix with a determinant of $0$ is called a singular matrix. Therefore,a skew-symmetric matrix of odd order is always singular.

Which one of the following statements is correct regarding skew-symmetric matrices?

Similar Questions

Let $A + 2B = \begin{bmatrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{bmatrix}$ and $2A - B = \begin{bmatrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{bmatrix}$. Then $Tr(A) - Tr(B)$ has the value equal to:

If $ A=\begin{bmatrix} \cos 2 \theta & -\sin 2 \theta \\ \sin 2 \theta & \cos 2 \theta \end{bmatrix} $ and $ A+A^{T}=I $,where $ I $ is the $ 2 \times 2 $ identity matrix and $ A^{T} $ is the transpose of $ A $,then the value of $ \theta $ is equal to

If $A$ and $B$ are symmetric matrices,then $ABA$ is

For the matrix $A = \begin{bmatrix} 1 & 5 \\ 6 & 7 \end{bmatrix}$,verify that $(A - A^{\prime})$ is a skew-symmetric matrix.

Identify the incorrect statement in respect of two square matrices $A$ and $B$ conformable for sum and product.

Vedclass Test Series

Exam Paper Generator

Online Exam Module