Determinants Questions (2072)

If \(\det(A)\)=4, then det(A\)^5A^5A⁻^9) equals:

If the system of linear equations 2x + 2ay + az = 0 2x + 3by + bz = 0 2x + 4cy + cz = 0 where a, b, c ∈ R are non-zero and distinct; has a non-zero solution, then :

If the system of equation, a2x - ay = 1 - a & bx + (3 - 2b)y = 3 + a possess a unique solution x = 1, y = 1 than :

If the system of linear equations x1 + 2x2 + 3x3 = 6 x1 + 3x2 + 5x3 = 9 2x1 + 5x2 + ax3 = b is consistent and has infinite number of solutions, then :-

Which of the following is an orthogonal matrix -

The set of all values of λ for which the system of linear equations 2x1 - 2x2 + x3 = λx1, 2x1 - 3x2 + 2x3 = λx2, -x1 + 2x2 = λx3 has a non-trivial solution

The determinant <mfenced open="|

Let f(x) = 1+sin2xcos2x4sin2xsin2x1+cos2x4sin2xsin2xcos2x1+4sin2x, then the maximum value of f(x), is-

If \(\det(A)\)=k, then det(A\)^nA^mA⁻^nA⁻^m) equals:

If the system of linear equations x + ky + 3z = 0 3x + ky - 2z = 0 2x + 4y - 3z = 0 has a non-zero solution (x, y, z), then xzy2 is equal to :

If \(\det(A)\)=2, then det(A\)^3A^2A⁻^3) equals:

If \(\det(A)\)=3, then det(A\)^4A^3A⁻^4) equals:

If \(\det(A)\)=4, then det(A\)^5A^2A⁻^5) equals:

If P is a 3 × 3 real matrix such that PT = aP + (a-1)I, where a > 1, then

If \(\det(A)\)=5, then det(A\)^6A^3A⁻^6) equals:

If \(\det(A)\)=k, then det(A\)^nA^mA⁻^n) where m>0 equals:

If \(\det(A)\)=5, then det(A\)^7A^4A⁻^4A⁻^7A^5A⁻^5) equals:

If x ≠ y ≠ z & x, y, z are in A.P. and D = 0, then 2xy^2z + x^2z^2 is equal to-

If \(\det(A)\)=4, then det((A\)^5A⁻^5)^6) equals:

If \(\det(A)\)=2, then det(A\)^3(A\)⁻^3 + \(I)) equals:

If A and B are two orthogonal matrices of order 3, then -(A) A and B both will be invertible matrices(B) matrix ABA will also be orthogonal(C) matrix A^2B^2 will also be orthogonal(D) maximum value of det\left(\frac{A}{2} adj(2B)\right) is 8.

If \(\det(A)\)=2, then det(A\)^3(A\)⁻^3 + \(I)^2) equals:

Let A = 12322-130k and f(x) = x3 - 2x2 - αx + β = 0. If A satisfies f(x) = 0, then-

Let A = \begin{pmatrix} 1 \\ 1 \\ 1 \end{pmatrix} and B = \begin{pmatrix} 9^2 & -10^2 & 11^2 \\ 12^2 & 13^2 & -14^2 \\ -15^2 & 16^2 & 17^2 \end{pmatrix}, then the value of A'BA is:

If x ≠ y ≠ z & x, y, z are in GP and D = 0, then y is equal to -

Let $p, q, r$ be real numbers such that $p + q + r \neq 0$. The system of linear equations$x + 2y - 3z = p$$2x + 6y - 11z = q$$x - 2y + 7z = r$has at least one solution if :

Matrix A = x321y422z, if xyz = 60 and 8x + 4y + 3z = 20, then A(adj A) is equal to -

The number of real values of x satisfying <mfenced open="|

$\text{tr}(A)$ is equal to

Let A = \begin{pmatrix} m & n \\ p & q \end{pmatrix}, d = |A| \neq 0, |A - d(\text{adj } A)| = 0. Then

If P = \begin{pmatrix} 1 & 0 \\ 1/2 & 1 \end{pmatrix}, then P^{50} is:

If $A = \begin{bmatrix}3&-3&4\\2&-3&4\\0&-1&1\end{bmatrix}$ and $B$ is the adjoint of $A$, then $\det(AB+2I)$ is (where $I$ is $3\times3$ identity)

If \(\det(A)\)=k, then det(A\)^n(I\) - \(A\)⁻^n)(I\) + \(A\)⁻^n)(I\) - \(A\)⁻^n)^p(I\) + \(A\)⁻^n)^q) equals:

22. $D = \begin{vmatrix} 10^4 + 2 & 10^7 + 3 & 10^8 + 8 \\ 10^9 + 9 & 10^2 + 8 & 10^3 - 4 \\ 10^3 - 5 & 10^8 + b & 10^6 + a \end{vmatrix}$ where $a, b$, both $\in \{1,2,3,4,5,6,7,8,9\}$Number of ordered pairs $(a, b)$ such that $D = 2n + 1, n \in Z$ is

If \(\det(A)\)=4, then det(A\)^5(A\)⁻^5 + \(I)(A\)⁻^5 - \(I)) equals:

If \(\det(A)\)=4, then det(A\)^5(A\)⁻^5 + \(I)(A\)⁻^5 - \(I)(A\)⁻^5 + \(I)) equals:

If x ≠ y ≠ z & x, y, z are in A.P. and D = 0, then 2xy^2z + x^2z^2 is equal to-

If sin22xcos2x4sin2x2tan2x2cos2x-sin2x-2cos4xtan2x2sin4x = a0 + a1(cosx) + a2(cos2x) + ........ + an(cosn x), then a0 is -

If \(\det(A)\)=4, then det(A\)^5(I\) - \(A\)⁻^5)(I\) + \(A\)⁻^5)(I\) - \(A\)⁻^5)) equals:

The determinant cos(θ+ϕ)-sin(θ+ϕ)cos2ϕsinθcosθsinϕ-cosθsinθcosϕ is -

If \(\det(A)\)=5, then det(A\)^6(I\) - \(A\)⁻^6)(I\) + \(A\)⁻^6)(I\) - \(A\)⁻^6)) equals:

For $\alpha,\beta\in\mathbb{R}$, suppose the system $x-y+z=5$, $2x+2y+\alpha z=8$, $3x-y+4z=\beta$ has infinitely many solutions. Then $\alpha$ and $\beta$ are roots of:

If \(\det(A)\)=k, then det(I\)\cdotA) equals:

If \(A\) is identity matrix, then det(A\)^n) equals:

If \(\det(A)\)=k, then det(A\)^0) equals:

Let A be a $n \times n$ matrix such that $|A| = 2$. If the determinant of the matrix $\text{Adj}(2 \cdot \text{Adj}(2A^{-1}))$ is $2^{84}$, then $n$ is equal to ___.

Let \(A = \begin{pmatrix} 0 & 2q & r \\ p & q & -r \\ p & -q & r \end{pmatrix}\). If \(AA^T = I_3\), then \(|p|\) is

If a2 + b2 + c2 = -2 and f(x) = 1+a2x(1+b2)x(1+c2)x(1+a2)x1+b2x(1+c2)x(1+a2)x(1+b2)x1+c2x then f(x) is a polynomial of degree-

Let \(0

If determinant is product of two matrices, then: