" 13."|[3x+y,2x,x],[4x+3y,3x,3x],[5x+6y,4x,6x]|=x^(3)

Without expanding the following determinant, show that : |[[3x+y, 2x, x],[4x+3y, 3x, 3x],[5x+6y,4x,6x]]|=x^3

Prove that |[x+y, x, x],[5x+4y, 4x, 2x], [10x+8y, 8x, 3x]|=x^3

Prove that: |[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3 .

|{:(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x):}|=x^3

Using properties of determinants, prove that |(x+y, x,x),(5x + 4y ,4x, 2x),(10x+8y,8x,3x)| = x^(3) .

Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x)|=x^3

Prove that |{:(x,x+y,x+y+z),(2x,3x+2y,4x+3y+2z),(3x,6x+3y,10x+6y+3z):}|=x^3

Prove that |{:(x,x+y,x+y+z),(2x,3x+2y,4x+3y+2z),(3x,6x+3y,10x+6y+3z):}|=x^3