Using properties of determinants, solve for `x:|a+x a-x a-x a-x a+x a-x a-x a-x a+x|=0`

Using properties of determinants, solve for x:|[a+x, a-x, a-x],[ a-x, a+x, a-x],[ a-x, a-x, a+x]|=0

Using properties of determinatnts solve the ,a+xquad a-xquad a-x,a+x,a-x,a-xa-x,a-x,a+x]|=0

Using properties of determinants,solve |(x+a,x,x),(x,x+a,x),(x,x,x+a)|=0

Using properties of determinants, solve the following for x: |[x-2, 2x-3, 3x-4],[x-4, 2x-9, 3x-16],[ x-8, 2x-27, 3x-64]|=0

Using properties find (x+3)(x-4).

By using properties of determinants, prove that the determinant |(a,sin x,cos x),(-sin x,-a,1),(cos x,1,a)| is independent of x.

Using properties of determinants, prove the following: |[1,x,x^2],[x^2, 1,x],[x,x^2,1]|=(1-x^3)^2

Solve: det[[a+x,a-x,a-xa-x,a+x,a-xa-x,a-x,a+x]]=0

Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+x),(4+x,4-x,4+x),(4-x,4+x,4+x)|=0

Using properties of determinants, prove the following |[x,x+y,x+2y],[x+2y,x,x+y],[x+y,x+2y,x]|=9y^2(x+y)