Question

the value of k such that the matrix (1 k/-k 1) is symmetry is​

Answer 1

SOLUTION

TO DETERMINE

The value of k such that

$\displaystyle\begin{pmatrix} 1 & k\\ - k & 1 \end{pmatrix}$

is symmetric

CONCEPT TO BE IMPLEMENTED

A Matrix M is said to be symmetric matrix if

$\sf{{M }^{t} =M }$

EVALUATION

Let

$M = \displaystyle\begin{pmatrix} 1 & k\\ - k & 1 \end{pmatrix}$

Now

${M}^{t} = \displaystyle\begin{pmatrix} 1 & - k\\ k & 1 \end{pmatrix}$

So by the given condition

$\sf{{M }^{t} =M }$

$\implies \displaystyle\begin{pmatrix} 1 & k\\ - k & 1 \end{pmatrix} = \displaystyle\begin{pmatrix} 1 & - k\\ k & 1 \end{pmatrix}$

$\implies \: k = - k$

$\implies \: 2k = 0$

$\implies \: k = 0$

FINAL ANSWER

The required value of k is 0

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