Determinants Te...

If A² - 2A - I = 0,then inverse of A is:

If a matrix A has inverses B and C, then which one of the following is correct?

For what values of \(k\), the equations:

\(x+y+z=1\)

\(2 x+y+4 z=k\)

\(4 x+y+10 z=k^{2}\)

have a solution?

Find the value of \(k\) if \(|A|=k\) such that \(A=\left[\begin{array}{cc}2 \cos x & -2 \sin x \\ \sin x & \cos x\end{array}\right]\)?

If a matrix A is such that 3A3+2A2+5A+I=0 then what is A−1 equal to?

For what value of \(\alpha \in R\) the system of equation: \(x+2 y+z=3,2 x+4 y+2 z=6\) and \(\alpha x+ \alpha y+ \alpha z=3\alpha\) has infinitely many solutions.

The system of equations:

\(2 x+y-3 z=5\)

\(3 x-2 y+2 z=5\) and

\(5 x-3 y-z=16\)

If \(A ^{-1}=\left[\begin{array}{lll}1 & 2 & 3 \\ 2 & 4 & 3 \\ 3 & 1 & 6\end{array}\right]=\frac{\operatorname{adj}( A )}{ k }\), then \(k =?\)

Find the value of \(\left|\begin{array}{lll}0 & c & b \\ c & 0 & a \\ b & a & 0\end{array}\right|^{2}\)

The cofactor of the element 4 in the determinant \(\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 5 & 8 & 9\end{array}\right]\) is:

If \(\mathrm{A}=\left[\begin{array}{ll}1 & 3 \\ 4 & 2\end{array}\right], \mathrm{B}=\left[\begin{array}{cc}2 & -1 \\ 1 & 2\end{array}\right]\), then \(\left|\mathrm{ABB}^{\prime}\right|=\)

Find the cofactor matrix for the matrix \(A=\left[\begin{array}{ccc}-1 & 2 & 3 \\ -2 & 3 & 5 \\ 4 & -2 & 1\end{array}\right]\)?

What is the value of the determinant \(\left|\begin{array}{ccc}\mathrm{i} & \mathrm{i}^{2} & \mathrm{i}^{3} \\ \mathrm{i}^{4} & \mathrm{i}^{6} & \mathrm{i}^{8} \\ \mathrm{i}^{9} & \mathrm{i}^{12} & \mathrm{i}^{15}\end{array}\right|\) where \(\mathrm{i}=\sqrt{-1}\)?

The solution of the matrix equation \(\left[\begin{array}{ccc}2 & -1 & 3 \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}9 \\ 6 \\ 2\end{array}\right]\) is:

If \(a_{1}, a_{2}, a_{3},=t_{9}, a_{9}\) are in GP, then what is the value of the following determinant?

\(\left|\begin{array}{lll}\ln a_{1} & \ln a_{2} & \ln a_{3} \\ \ln a_{4} & \ln a_{5} & \ln a_{6} \\ \ln a_{7} & \ln a_{8} & \ln a_{9}\end{array}\right|\)

If \({A}=\left[\begin{array}{ll}{x} & 2 \\ 4 & {x}\end{array}\right]\) and det \(\left(A^{2}\right)=64\), then \({x}\) is equal to:

Let A be a non-singular matrix of the order 2 × 2 then |A^-1| =

Find the area of triangle with vertices at points A (1, 1) ,B ( 6, 0) and C ( 3, 2).

Find \(M_{13} \times C_{21}+C_{33} \times C_{31}\) for the given matrix \(A=\left[\begin{array}{ccc}2 & -3 & 4 \\ 1 & 0 & -1 \\ 3 & 1 & -2\end{array}\right]\), where \(M_{i j}\) and \(C_{i j}\) are the respective minor and co-factor of the element \(a_{i j}\)?

If the system of equation \(2 x+3 y+5=0, x+k y+5=0, k x-12 y-14=0\) be consistent, then the values of \(k\) are:

If A is a square matrix, then what is adj A^T - (adj A)^T equal to?

\(2 x-3 y=0\) and \(2 x+\alpha y=0\)

For what value of \(\alpha\) the system has infinitely many solution.

If \(\omega\) is the cube root of unity, then what is the value of:

\(\left|\begin{array}{ccc}1 & \omega & \omega^{2} \\ \omega & \omega^{2} & 1 \\ \omega^{2} & 1 & \omega\end{array}\right|\)

Find the \((\operatorname{adj} A)\), if:

\(A=\left[\begin{array}{lll}3 & 7 & 1 \\ 2 & 1 & 8 \\ 4 & 5 & 0\end{array}\right]\)

If \(A=\left[\begin{array}{lll}8 & 7 & 0 \\ 6 & 5 & 4 \\ 3 & 2 & 1\end{array}\right]\), then find the value of \(\left|A^{-1}\right|\).

Consider the following in respect of a non-singular matrix of order 3:

1. A (adj A) = (adj A) A

2. |adj A| = |A|

Which of the above statements is / are correct?

If \(x,y,z\) are all different and not equal to zero and \(\left|\begin{array}{ccc}1+x & 1 & 1 \\ 1 & 1+y & 1 \\ 1 & 1 & 1+z\end{array}\right|=0\) then the value of \(x^{-1}+y^{-1}+z^{-1}\) is equal to:

Find the area of the triangle with vertices (1, -2), (3, 1) and (2, 4).

Find the solution set of p if the given system of linear equations is inconsistent.

\(3 x+3 y+3 z=3\)

\(3 x+6 y+12 z=3 p\)

\(3 x+12 y+30 z=3 p ^2\)