Question

If f is an invertible function, defined as f(x) = $\frac{3x-4}{5}$, then write $f^{-1}(x).$

For what value of x, the given matrix A = $\left(\begin{array}{l l }3-2x & x+1 \\ 2 & 4\end{array}\right)$ is a singular matrix ?

If A = $\left(\begin{array}{l l }cosα & sinα \\ -sinα & cosα\end{array}\right)$ , find α satisfying $0\leq\alpha\leq{\frac{\pi}{4}}$ when $A+A^{T}=\sqrt{2}I$ where $A^{T}$ is transpose of A.

Write the value of x + y + z if $\left(\begin{array}{l l l }1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right)$ $\left(\begin{array}{l }x \\ y \\ z\end{array}\right)$ = $\left(\begin{array}{l }1 \\ -1 \\ 0\end{array}\right)$.

Write a unit vector in the direction of vector $\stackrel{\rightarrow}{PQ}\$ where $\stackrel{\rightarrow}{p}\$ and $\stackrel{\rightarrow}{q}\$ are the points (1, 3, 0) and (4, 5, 6),respectively,

If A is an invertible square matrix of order 3 and |A| = 5, then find the value of |adj A|.

Let R be the equivalence relation in the set A = {0, 1, 2, 3, 4, 5} given by R = {(a, b) : 2 divides (a –b)}. Write the equivalence class [0].