Advertisements
Advertisements
Question
Evaluate the following determinant:
`|("a", "h", "g"),("h", "b", "f"),("g", "f","c")|`
Solution
`|("a", "h", "g"),("h", "b", "f"),("g", "f","c")|`
= `"a"|("b", "f"),("f","c")| - "h"|("h","f"),("g","c")| + "g"|("h","b"),("g", "f")|`
= a(bc – f2) – h(hc – gf) + g(hf – gb)
= abc – af2 – h2c + fgh + fgh – g2b
= abc + 2fgh – af2 – bg2 – ch2
APPEARS IN
RELATED QUESTIONS
Evaluate the following determinants: `|(3, -4, 5),(1, 1, -2),(2, 3, 1)|`
Evaluate the following determinant:
`|(0, "a", -"b"),(-"a", 0, -"c"),("b", "c", 0)|`
Evaluate: `|(2, -5, 7),(5, 2, 1),(9, 0, 2)|`
The value of `|(2x + y,x,y),(2y+z,y,z),(2z+x,z,x)|` is
If `Delta = |(1,2,3),(3,1,2),(2,3,1)|` then `|(3,1,2),(1,2,3),(2,3,1)|` is
If A is square matrix of order 3 then |kA| is
The value of `|(x,x^2 - yz,1),(y,y^2-zx,1),(z,z^2-xy,1)|` is
Solve: `|(x,2,-1),(2,5,x),(-1,2,x)|` = 0
Show that `|(0,ab^2,ac^2),(a^2b,0,bc^2),(a^2c,b^2c,0)| = 2a^3b^3c^3`
Evaluate the following determinant :
`|(4,7),(-7,0)|`
Evaluate the following determinant :
`|(3,-5,2),(1,8,9),(3,7,0)|`
Without expanding evaluate the following determinant.
`|(1,a,a + c),(1,b,c + a),(1,c,a + b)|`
Evaluate the following determinant :
`|(4,7),(-7,0)|`
Evaluate the following determinant:
`|(4,7),(-7,0)|`
Evaluate the following determinant:
`|(4 ,7),(-7 ,0)|`
Evaluate the following determinant:
`|(4,7),(-7,0)|`
Find the value of x if `|(x,-1,2),(2x,1,-3),(3,-4,5)|` = 29
Find the value of x if `|(x, 2x, 3),(-1, 1, -4),(3, -3, 5)|` = 29
Evaluate the following determinant:
`[(a, h, g),(h, b, f),(g, f, c)]`
Find the value of x if `|(x,-1,2),(2x,1,-3),(3,-4,5)|` = 29.
