The determinant | array ccc a & b & a +b b & c & b +c a +b & b +c & 0 array | is equal to…
Mathematics · JEE Advanced · NTA Exams — Matrices and Determinants
The determinant \[\left|\begin{array}{ccc}
a & b & a \alpha+b \\
b & c & b \alpha+c \\
a \alpha+b & b \alpha+c & 0
\end{array}\right|\] is equal to zero, if
- a, b, c are in A.P.
- a, b, c are in G.P.
- a, b, c are in H.P.
- α is a root of the equation ax2 + bx + c = 0
- (x – α) is a factor of ax2 + 2bx + c
Answer
(B) a , b , c are in G . P.
Sign up free on Edukali to view the step-by-step worked solution and practice thousands of similar questions.
Related practice questions
- Let M be a 3 × 3 invertible matrix with real entries and let I denote the 3 × 3 identity matrix. If M −1 =…
- If a 2 + b 2 + c 2 = 1, then | array ccc a^ 2 + (b^ 2 +c^ 2 ) & b(1- ) & a(1- ) a(1- ) & b^ 2 + (c^ 2 +a^ 2 )…
- If the system of equations x – ky – z = 0, kx – y – z = 0, x + y – z = 0 has a non-zero solution, then…
- Let ∆ = 0 and ∆ c denotes the determinant of cofactors, then ∆ c = ∆ n – 1 , where n (> 0) is the order of ∆…
- If x N and ^ x C _ i , ^ x ^ 2 C _ i and x^ 3 C_ i , (i = 1, 2, 3) are binomial coefficients, then 12 | array…
- Suppose a, b, c are distinct real numbers. Let f(x)= | array lll x^ 3 +a^ 3 & x^ 2 -a^ 2 & x+a x^ 3 +b^ 3 &…
- If P= [ array cc 3 2 & 1 2 - 1 2 & 3 2 array ], A= [ array ll 1 & 1 0 & 1 array ] and Q = PAP T , then P T (…
- The system of equations αx + y + z = α – 1 x + αy + z = α – 1 x + y + αz = α –1 has no solution, if α is :
More Matrices and Determinants questions · Browse all practice questions