[y+k,y,y],[y,y+k,y],[y,y,y+k]|=k^(2)(3y+k)

Prove that abs[[y+k,y,y],[y,y+k,y],[y,y,y+k]]=k^2(3y+k)

By using properties of determinants. Show that: (i) |(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4)|=(5x-4)(4-x)^2 (ii) |(y+k,y,y),(y,y+k,y),(y,y,y+k)|=y^2(3y+k)

By using properties of determinants , show that : (i) {:[( x+4, 2x, 2x),( 2x,x+4, 2x),( 2x,2x, x+4) ]:}=( 5x +4) (4-x)^(2) ( ii) {:[( y+k , y , y ),( y,y+ k , y ),( y,y , y+k ) ]:} =k^(2) ( 3y +k )

Using properties of determinants , find the value of k if |{:(x,y,x+y),(y,x+y,x),(x+y,x,y):}|=k(x^(3)+y^(3)) .

If ([y+z,x,yz+x,z,xx+y,y,z])=k(x-z)^(2), then find K