Question

Let A = {1, 2, 3, 4}. Let R be the equivalence relation on A × A defined by (a, b)R(c, d) if a + d = b + c. Find the equivalence class [(1,3)].

If $(2x\ \ 4){\binom{x}{-8}}=0,$ find the positive value of x.

If a unit vector $\stackrel{\rightarrow}{a}\$ makes an angle $\frac{\pi}{3}$ with $\stackrel{\wedge}{i},$ $\frac{\pi}{4}$ with $\stackrel{\wedge}{j}$ and an acute angle θ with $\stackrel{\wedge}{k}$, then find the value of θ.

Write a vector in the direction of the vector $\displaystyle{\hat{\iota}}-2\,{\hat{\iota}}+2\,{\hat{\iota}}$ that has magnitude 9 units.

If $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$ are unit vectors, then what is the angle between $\stackrel{\rightarrow}{a}\$ and $\stackrel{\rightarrow}{b}\$, so that ${\sqrt{2}}$ $\stackrel{\rightarrow}{a}\$ -$\stackrel{\rightarrow}{b}\$ is a unit vector ?

If A is a square matrix such that A² = A, then write the value of (I + A)² – 3A.

If $\left(\begin{array}{l l }1 & 2 \\ 3 & 4\end{array}\right)$ $\left(\begin{array}{l l }3 & 1 \\ 2 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 11 \\ k & 23\end{array}\right)$ , then write the value of k.