Advertisements
Advertisements
Question
Without actual expansion show that the value of the determinant `|(5,5^2,5^3),(5^2,5^3,5^4),(5^4,5^5,5^6)|` is zero.
Solution
Taking 5, 52 and 54 common from R1, R2 and R3 respectively we get
`|(5,5^2,5^3),(5^2,5^3,5^4),(5^4,5^5,5^6)| = 5 xx 5^2 xx 5^4 |(1,5,5^2),(1,5,5^2),(1,5,5^2)|`
= 5 × 5^2 × 5^4 × 0 = 0 ....[R1 ≡ R2 ≡ R3]
APPEARS IN
RELATED QUESTIONS
Evaluate the following determinant:
`|(0, "a", -"b"),(-"a", 0, -"c"),("b", "c", 0)|`
Find the value of x, if `|(x, -1, 2),(2x, 1, -3),(3, -4, 5)|` = 29
Find the minors and cofactors of all the elements of the following determinant.
`|(5,20),(0, -1)|`
If A = `|(cos theta,sin theta),(-sin theta,cos theta)|`, then |2A| is equal to
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
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)|`
Find the value of x if `|(x, 2x, 3),(-1, 1, -4),(3, -3, 5)|` = 29
