Question

if the two matrices [1 0 x 0 x 1 0 1 x] and [x 1 0 x 0 1 0 x 1] have the same determinant then the value of X is

Comments

is it?

$\begin{bmatrix} 1 &0 &x \\ 0&x &1 \\ 0 & 1 &x \end{bmatrix}$ and $\begin{bmatrix} x &1 &0\\ x&0&1 \\ 0 & x &1 \end{bmatrix}$

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but it has same determinant as mentioned in the question

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ya its simple .

$\begin{vmatrix} 1 &0 &x \\ 0&x &1 \\ 0 & 1 &x \end{vmatrix}$=$x^{2}-1$

$\begin{vmatrix} x &1 &0\\ x&0&1 \\ 0 & x &1 \end{vmatrix}$=$-x^{2}-x$

Given that determinant is same So

$x^{2}-1=-x^{2}-x$

$2x^{2}+x-1=0$

Solve the equation you will get $x=-1$ and $x=1/2$ .

Answer 1

1 0 x              x 1 0  

0 x 1              x 0 1

0 1 x              0 x 1

for first matrix take by c1  

=1(x²-1)-0+0

=x²=1 ie x=1

for second matrix

i took first row

=x(0-x)-1(x-0)+0

= -x²-x

ie x=-1

it doesn't have same determinant