Determinants · Mathematics · NDA

For what value of $n$ is the determinant $$ \left|\begin{array}{ccc} C(9,4) & C(9,3) & C(10, n-2) \\ C(11,6) & C(11,5) & C(12, n) \\ C(m, 7) & C(m, 6)...

If ABC is a triangle, then what is the value of the determinant $$ \left|\begin{array}{ccc} \cos C & \sin B & 0 \\ \tan A & 0 & \sin B \\ 0 & \tan (B+...

If $a, b, c$ are the sides of a triangle $ABC$, then what is $$ \begin{vmatrix} a^2 & b \sin A & c \sin A \\ b \sin A & 1 & \cos A \\ c \sin A & \cos ...

If in a triangle $ABC$, $\sin^3A + \sin^3B + \sin^3C = 3\sin A \sin B \sin C$, then what is the value of the determinant $\begin{vmatrix} a & b & c \\...

If $A=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right]$, then what is the value of det(I + AA'), where I is the 3 × 3 identity matrix?...

If A, B and C are square matrices of order 3 and det(BC) = 2 det(A), then what is the value of det(2A-1BC)?

Let A be a skew-symmetric matrix of order 3. What is the value of det(4A4) - det(3A3) + det(2A2) - det(A) + det(-I)  where I is the identit...

If $A=\left[\begin{array}{rrr} 0 & 3 & 4 \\ -3 & 0 & 5 \\ -4 & -5 & 0 \end{array}\right]$, then which one of the following sta...

If $\left|\begin{array}{ccc} x^2+3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x \end{array}\right|$ = a...

If all elements of a third order determinant are equal to 1 or -1, then the value of the determinant is:

If $A=\left[\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 3 & 0 \\ 1 & 0 & 1 \end{array}\right]$, then what is the value of det[a...

The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of deter...

If $A_k=\left[\begin{array}{cc} k-1 & k \\ k-2 & k+1 \end{array}\right] $, then what is det(A1) + det(A2) + det(A3) + ... + det(A100...

The function is decreasing on :

The function attains local minimum value at :

Let A be a matrix of order 3 × 3 and |A| = 4. If |2adj(3A)| = 2α 3β, then what is the value of (α + β)? 

What is the sum of the roots of the equation $\left|\begin{array}{ccc} 0 & x-a & x-b \\ 0 & 0 & x-c \\ x+b & x+c & 1 \end...

If a, b, c are in AP, then what is $\left|\begin{array}{lll} x+1 & x+2 & x+3 \\ x+2 & x+3 & x+4 \\ x+a & x+b & x+c \end{a...

If Δ(a, b, c, α) = 0 for every α > 0, then which one of the following is correct ? 

If Δ(7, 4, 2, α) = 0, then α is a root of which one of the following equations ? 

Consider the determinant Δ = $\left|\begin{array}{lll}\text{a}_{11} & \text{a}_{12} & \text{a}_{13} \\ \text{a}_{21} & \text{a}_{22}...

What is the value of a11C11 + a12C12 + a13C13 ? ...

What is the value of $a_{21}C_{11}+a_{22}C_{12}+a_{23}C_{13}$?

What is the value of $\left|\begin{array}{lll}\text{a}_{21} & \text{a}_{31} & \text{a}_{11} \\ \text{a}_{23} & \text{a}_{33} & \t...

What is the minimum value of determinant of A ?

If $Δ_1 = \begin{vmatrix} 1 & p & q \\ 1 & q & r \\ 1 & r & p\end{vmatrix} \ \text{and} \ Δ_2 = \begin{vmatrix} 1 & 1...

If (a - b) (b - c) (c - a) = 2 and abc = 6, then what is the value of $\begin{vmatrix}a & b & c \\ a^2 & b^2 & c^2 \\ a^3 & b...

Under which of the following conditions does the determinant $\begin{vmatrix}a & b & c \\ b & c & a \\ c & a & b\end{vmat...

For what value of k is the matrix $\begin{bmatrix} 2\cos 2\theta & 2\cos 2\theta & 6 \\ 1 -2 \sin^2\theta & 2 \cos^2\theta -1 & 3...

If A is the identity matrix of order 3 and B is its transpose, then what is the value of the determinant of the matrix C = A + B?