Question

If A and B are invertible matrices of order 3, $|\mathbf{A}|=$ 2 and $|(\mathbf{AB})^{-1}|\,=\,-{\frac{1}{6}}.$ Find $|\mathbf{B}$.

For what value of λ are the vectors $\stackrel{\wedge}{i}+2λ \stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $2\stackrel{\wedge}{i}+\stackrel{\wedge}{j} -3\stackrel{\wedge}{k}$ perpendicular ?

If x ∈ N and $\begin{vmatrix}x+3 & -2 \\ -3x & 2x\end{vmatrix}$ = 8, then find the value of x.

Evaluate $\textstyle\int$ sin³ x dx.

If x $\left(\begin{array}{l }2 \\ 3\end{array}\right)$ + y $\left(\begin{array}{l }-y \\ y\end{array}\right)$ = $\left(\begin{array}{l }10 \\ 5\end{array}\right)$ , write the value of x.

State the reason for the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} not to be transitive.

Let f : R → R be defined by f(x) = 3x² – 5 and g : R → R be defined by g(x) =${\frac{x}{x^{2}+1}}.$ find gof(x) .