Evaluate the following: ` |[1,,a^2-bc],[1, b,b^2-ac],[1,c,c^2-ab]| `

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

Without expanding, show that the value of each of the determinants is zero: |[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|

Evaluate [[a,a^2-bc,1],[b,b^2-ac,1],[c,c^2-ab,1]]

Prove the following: [[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]] =1+a^2+b^2+c^2

Prove the following: [[-a^2,ab,ac],[ab,-b^2,bc],[ac,bc,-c^2]]=4a^2b^2c^2

Find the value of det[[1,a,a^(2)-bc1,b,b^(2)-ac1,c,c^(2)-ab]]

det[[1,a,a^(2)+bc1,b,b^(2)+ac1,c,c^(2)+ab]] is equal to

Find the value of : |(1/a,a^2,bc),(1/b,b^2,ca),(1/c,c^2,ab)|

Using properties of determinants, prove the following |(a^2,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .

Using properties of determinants, prove the following |(a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|=1+a^2+b^2+c^2 .