Advertisements
Advertisements
Question
Evaluate the following determinant:
`|(0, "a", -"b"),(-"a", 0, -"c"),("b", "c", 0)|`
Solution
`|(0, "a", -"b"),(-"a", 0, -"c"),("b", "c", 0)|`
= `0|(0, -"c"),("c", 0)| -"a"|(-"a", - "c"),("b", 0)| -"b"|(-"a", 0),("b", "c")|`
= 0 – a (0 + bc) – b(– ac – 0)
= – a(bc) – b (– ac)
= – abc + abc
= 0
APPEARS IN
RELATED QUESTIONS
Evaluate the following determinants: `|(5, 5, 5),(5, 4, 4),(5, 4, 8)|`
Evaluate the following determinants: `|(2"i", 3),(4, -"i")|`
Find x and y if `|(4"i", "i"^3, 2"i"),(1, 3"i"^2, 4),(5, -3, "i")|` = x + iy, where i = `sqrt(-1)`.
Without expanding evaluate the following determinant:
`|(2, 3, 4),(5, 6, 8),(6x, 9x, 12x)|`
Evaluate: `|(1,a,a^2 - bc),(1,b,b^2 - ca),(1,c,c^2 - ab)|`
Prove that `|(1/a,bc,b+c),(1/b,ca,c+a),(1/c,ab,a+b)|` = 0
The value of the determinant `[(a,0,0),(0,b,0),(0,0,c)]^2` is
If A is a square matrix of order 3 and |A| = 3 then |adj A| is equal to:
The value of `|(x,x^2 - yz,1),(y,y^2-zx,1),(z,z^2-xy,1)|` is
Evaluate the following determinants :
`|(4,7),(-7,0)|`
Evaluate the following determinant :
`|(3,-5,2),(1,8,9),(3,7,0)|`
Find the value of x if
`|(x, -1, 2),(2x, 1 , -3) ,(3, -4, 5)|` = 29
Evaluate the following determinant :
`|(3,-5,2),(1,8,9),(3,7,0)|`
Evaluate the following determinant:
`|(3,-5,2),(1,8,9),(3,7,0)|`
Without expanding evaluate the following determinant.
`|(1,a,b+c),(1,b,c+a),(1,c, a+b)|`
Find the value of x if `|(x,-1,2),(2x,1,-3),(3,-4,5)|` = 29
Evaluate the following determinant:
`|(3, -5, 2), (1, 8, 9), (3, 7, 0)|`
Evaluate the following determinant:
`[(3, -5, 2),(1, 8, 9),(3, 7, 0)]`
Evaluate the following determinant:
`|(4, 7),(-7, 0)|`
