determinant

The eigenvalues of $[A] = \begin{bmatrix} 2 & -3.5 & 6 \\ 3.5 & 5 & 2 \\ 8 & 1 & 8.5 \end{bmatrix}$ are $\lambda_1 = -1.547$, $\lambda_2 = 12.330$, and $\lambda_3 = 4.711$. The abs...

Let $f(x) = \begin{vmatrix} x^3 & \sin x & \cos x \\ 6 & -1 & 0 \\ p & p^2 & p^3 \end{vmatrix}$ where $p$ is a constant. The value of $\frac{d^3}{dx^3} f(x)$ at $x = 0$ is

Consider two matrices A = $\begin{bmatrix} 2 & 1 & 4 \\ 1 & 0 & 3 \end{bmatrix}$ and B = $\begin{bmatrix} -1 & 0 \\ 2 & 3 \\ 1 & 4 \end{bmatrix}$. The determinant of the matrix AB...

Consider two matrices $A = \begin{bmatrix}2 & 1 & 4 \\ 1 & 0 & 3\end{bmatrix}$ and $B = \begin{bmatrix}-1 & 0 \\ 2 & 3 \\ 1 & 4 \end{bmatrix}$. The determinant of the matrix $AB$ i...

Which one of the following matrices is singular?

The smallest and largest Eigen values of the following matrix are : $$\left[ {\matrix{ 3 & { - 2} & 2 \cr 4 & { - 4} & 6 \cr 2 & { - 3} & 5 \cr } } \right]$$

The two Eigen Values of the matrix $$\left[ {\matrix{ 2 & 1 \cr 1 & p \cr } } \right]$$ have a ratio of $$3:1$$ for $$p=2.$$ What is another value of $$'p'$$ for which the Eigen va...

With reference to the conventional Cartesian $$(x,y)$$ coordinate system, the vertices of a triangle have the following coordinates: $$\,\left( {{x_1},{y_1}} \right) = \left( {1,0}...

The determinant of matrix $$\left[ {\matrix{ 0 & 1 & 2 & 3 \cr 1 & 0 & 3 & 0 \cr 2 & 3 & 0 & 1 \cr 3 & 0 & 1 & 2 \cr } } \right]$$ is

The inverse of the matrix $$\left[ {\matrix{ {3 + 2i} & i \cr { - i} & {3 - 2i} \cr } } \right]$$ is

The following system of equations $$$x+y+z=3,$$$ $$$x+2y+3z=4,$$$ $$$x+4y+kz=6$$$ will not have a unique solution for $$k$$ equal to

Solution for the system defined by the set of equations $$4y+3z=8, 2x-z=2$$ & $$3x+2y=5$$ is

For a given matrix $$A = \left[ {\matrix{ 2 & { - 2} & 3 \cr { - 2} & { - 1} & 6 \cr 1 & 2 & 0 \cr } } \right],$$ one of the eigen value is $$3.$$ The other two eigen values are

Consider the following system of equations in three real variable $${x_1},$$ $${x_2}$$ and $${x_3}:$$ $$$2{x_1} - {x_2} + 3{x_3} = 1$$$ $$$3{x_1} + 2{x_2} + 5{x_3} = 2$$$ $$$ - {x_...

The determinant of the following matrix $$\left[ {\matrix{ 5 & 3 & 2 \cr 1 & 2 & 6 \cr 3 & 5 & {10} \cr } } \right]$$

If $$A$$ is any $$nxn$$ matrix and $$k$$ is a scalar then $$\left| {kA} \right| = \alpha \left| A \right|$$ where $$\alpha $$ is

If the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 2 \cr 0 & 5 & { - 6} \cr 2 & 7 & 8 \cr } } \right]$$ is $$26,$$ then the determinant of the matrix $$\left[ {\matrix{ 2...