Which of the following determinants have value 'zero'?
1. `|{:(41,1,5),(79,7,9),(29,5,3):}|`
2. `|{:(1,a,b+c),(1,b,c+a),(1,c,a+b):}|`
3. `|{:(0,c,b),(-c,0,a),(-b,-a,0):}|`
Select the correct answer using the code given below.

|{:(41,1,5),(79,7,9),(29,5,3):}|=0

Which of the following determinants have value 'zero' ? 1. |(41,1,5),(79,7,9),(29,5,3)| 2. [(1,a,b+c),(1,b,c+a),(1,c,a+b)] 3. [(0,c,b),(-c,0,a),(-b,-a,0)] Select the correct answer using the codes given below :

Without expanding,find the values of the following determinants: |(41,1,5),(79,7,9),(29,5,3)|

If a+b+c=0, then which of the following are correct? 1. a^(3) + b^(3) + c^(3) = 3abc 2. a^(2) + b^(2) + c^(2) = -2(ab + bc + ca) 3. a^(3) + b^(3) + c^(3) = -3ab(a+b) Select the correct answer using the code given below

If a and b are negative real numbers and c is a positive real number, then which of the following is/are correct? 1. a-b lt a-c 2. If a lt b , then (a)/(c ) lt (b)/(c ) . 3. (1)/(b) lt (1)/(c ) Select the correct answer using the code given below.

If a+b+c=0 , then which of the following is/are correct? 1. a,b,c are coplanar 2. a xx b=b xx c=c xx a Select the correct answer using the codes given below

Using properties of determinants, prove that |(1,a,a^(3)),(1,b,b^(3)),(1,c,c^(3))| = (a-b)(b-c)(c-a)(a+b+c) .

Without expanding, prove that [[41,1,5],[79,7,9],[29,5,3]] =0

If [{:(,a,3),(,4,1):}]+[{:(,2,b),(,1,-2):}]-[{:(,1,1),(,-2,c):}] =[{:(,5,0),(,7,3):}] find the values of a,b and c.

If ({:(1, 0),(0, 1):})({:(a, b+c),(b-c, d):}) = ({:(4, -5),(3, 2):}) , then (a-b) + (c-d)=____.