Question

if A =[ 0 4 -2 -4 0 8 2 -8 X] is a skew symmetric matrix then find the value of x
​

Answer 1

SOLUTION

GIVEN

$A = \displaystyle\begin{pmatrix} 0 & 4 & - 2\\ - 4 & 0 & 8 \\ 2 & - 8 & x \end{pmatrix}$

is a skew symmetric matrix

TO DETERMINE

The value of x

CONCEPT TO BE IMPLEMENTED

A Matrix A is said to be skew symmetric matrix if

${A}^{t} = - A$

EVALUATION

Here it is given that

$A = \displaystyle\begin{pmatrix} 0 & 4 & - 2\\ - 4 & 0 & 8 \\ 2 & - 8 & x \end{pmatrix}$

$\implies \: {A}^{t} = \displaystyle\begin{pmatrix} 0 & - 4 & 2\\ 4 & 0 & - 8 \\ - 2 & 8 & x \end{pmatrix}$

Since A is a skew symmetric matrix

${A}^{t} = - A$

$\implies \: \displaystyle\begin{pmatrix} 0 & - 4 & 2\\ 4 & 0 & - 8 \\ - 2 & 8 & x \end{pmatrix} = - \displaystyle\begin{pmatrix} 0 & 4 & - 2\\ - 4 & 0 & 8 \\ 2 & - 8 & x \end{pmatrix}$

$\implies \: \displaystyle\begin{pmatrix} 0 & - 4 & 2\\ 4 & 0 & - 8 \\ - 2 & 8 & x \end{pmatrix} = \displaystyle\begin{pmatrix} 0 & - 4 & 2\\ 4 & 0 & - 8 \\ - 2 & 8 & - x \end{pmatrix}$

Comparing both sides we get

$x = - x$

$\implies 2x = 0$

$\implies x = 0$

Hence the required value of x is 0

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Answer 2

Answer:

SOLUTION

GIVEN

\begin{gathered}A = \displaystyle\begin{pmatrix} 0 & 4 & - 2\\ - 4 & 0 & 8 \\ 2 & - 8 & x \end{pmatrix} \end{gathered}A=⎝⎛0−4240−8−28x⎠⎞

is a skew symmetric matrix

TO DETERMINE

The value of x

CONCEPT TO BE IMPLEMENTED

A Matrix A is said to be skew symmetric matrix if

{A}^{t} = - AAt=−A

EVALUATION

Here it is given that

\begin{gathered}A = \displaystyle\begin{pmatrix} 0 & 4 & - 2\\ - 4 & 0 & 8 \\ 2 & - 8 & x \end{pmatrix} \end{gathered}A=⎝⎛0−4240−8−28x⎠⎞

\begin{gathered} \implies \: {A}^{t} = \displaystyle\begin{pmatrix} 0 & - 4 & 2\\ 4 & 0 & - 8 \\ - 2 & 8 & x \end{pmatrix} \end{gathered}⟹At=⎝⎛04−2−4082−8x⎠⎞

Since A is a skew symmetric matrix

{A}^{t} = - AAt=−A

\begin{gathered} \implies \: \displaystyle\begin{pmatrix} 0 & - 4 & 2\\ 4 & 0 & - 8 \\ - 2 & 8 & x \end{pmatrix} = - \displaystyle\begin{pmatrix} 0 & 4 & - 2\\ - 4 & 0 & 8 \\ 2 & - 8 & x \end{pmatrix} \end{gathered}⟹⎝⎛04−2−4082−8x⎠⎞=−⎝⎛0−4240−8−28x⎠⎞

\begin{gathered} \implies \: \displaystyle\begin{pmatrix} 0 & - 4 & 2\\ 4 & 0 & - 8 \\ - 2 & 8 & x \end{pmatrix} = \displaystyle\begin{pmatrix} 0 & - 4 & 2\\ 4 & 0 & - 8 \\ - 2 & 8 & - x \end{pmatrix} \end{gathered}⟹⎝⎛04−2−4082−8x⎠⎞=⎝⎛04−2−4082−8−x⎠⎞

Comparing both sides we get

x = - xx=−x

\implies 2x = 0⟹2x=0

\implies x = 0⟹x=0

Hence the required value of x is 0