Out of the following which is a skew- symmetric matrix

⎡ ⎢ ⎣ \begin{matrix} 0 & 4 & 5 - 4 & 0 & - 6 - 5 & 6 & 0 \end{matrix} ⎤ ⎥ ⎦

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

⎡ ⎢ ⎣ \begin{matrix} 1 & 4 & 5 - 4 & 1 & - 6 - 5 & 6 & 1 \end{matrix} ⎤ ⎥ ⎦

No worries! We‘ve got your back. Try BYJU‘S free classes today!

⎡ ⎢ ⎣ \begin{matrix} 1 & 4 & 5 - 4 & 2 & - 6 - 5 & 6 & 3 \end{matrix} ⎤ ⎥ ⎦

No worries! We‘ve got your back. Try BYJU‘S free classes today!

⎡ ⎢ ⎣ \begin{matrix} i + 1 & 4 & 5 - 4 & i & - 6 - 5 & 6 & i \end{matrix} ⎤ ⎥ ⎦

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $⎡ ⎢ ⎣ \begin{matrix} 0 & 4 & 5 - 4 & 0 & - 6 - 5 & 6 & 0 \end{matrix} ⎤ ⎥ ⎦$
In a skew-symmetrix matrix $a_{i j} = - a_{j i} \forall i, j = 1, 2, 3 f o r j = i, a_{i i} = - a_{j i} \Rightarrow$ each $a_{i i} = 0$ .
Hence the matrix $⎡ ⎢ ⎣ \begin{matrix} 0 & 4 & 5 - 4 & 0 & - 6 - 5 & 6 & 0 \end{matrix} ⎤ ⎥ ⎦$ is skew-symmetric.

Suggest Corrections

Similar questions

Q. Write matrix

A

as the sum of a symmetric and a skew symmetric matrix, where

A = ⎛ ⎜ ⎝ \begin{matrix} 4 & 2 & - 3 1 & 3 & - 6 - 5 & 0 & - 7 \end{matrix} ⎞ ⎟ ⎠

Q. Which of the following is terminating decimal?

\frac{23}{90}, \frac{111}{148}, \frac{29}{145}, \frac{1}{6}

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

⎡ ⎢ ⎣ \begin{matrix} 6 & - 2 & 2 - 2 & 3 & - 1 2 & - 1 & 3 \end{matrix} ⎤ ⎥ ⎦

Q. Express

⎡ ⎢ ⎣ \begin{matrix} 6 & - 4 & 5 1 & 4 & - 2 7 & 5 & 9 \end{matrix} ⎤ ⎥ ⎦

as a sum of a symmetric matrix and a skew-symmetric matrix.

Calculate the median from the following data:

$\begin{matrix} Height (in cm) & 135 - 140 & 140 - 145 & 145 - 150 & 150 - 155 & 155 - 160 & 160 - 165 & 165 - 170 & 170 - 175 Number of days & 6 & 10 & 18 & 22 & 20 & 15 & 6 & 3 \end{matrix}$

Join BYJU'S Learning Program

Out of the following which is a skew- symmetric matrix

The correct option is A ⎡⎢⎣045−40−6−560⎤⎥⎦In a skew-symmetrix matrix aij=−aji∀i,j=1,2,3 for j=i,aii=−aji⇒ each aii=0. Hence the matrix ⎡⎢⎣045−40−6−560⎤⎥⎦ is skew-symmetric.