Question

Write the value of x - y + z from following equation. $\left(\begin{array}{l }x+y+z \\ x+z \\ y+z\end{array}\right)$ = $\left(\begin{array}{l }9 \\ 5 \\ 7\end{array}\right)$

If $\stackrel{\rightarrow}{a}\$ =$4\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ =$2\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ then find a unit vector parallel to the vector $\stackrel{\rightarrow}{a}+\stackrel{\rightarrow}{b}$

Write the value of the determinant $\begin{vmatrix}p & p+1 \\ p-1 & p\end{vmatrix}$

Write the integrating factor of the differential equations ${\sqrt{x}}{\frac{d y}{d x}}+y=e^{-2{\sqrt{x}}}\,.$

If A is a square matrix such that A² = I, then find the simplified value of (A – I)³ + (A + I)³ – 7A.

If matrix A = $[a_{i j}]_{2\times2}$, where $a_{i j}$ = $\left\{\begin{array}{l}{{2,\ i\neq j}}\\ {{0,\ i=j^{\prime}}}\end{array}\right.$ , Write the matrix A.

Write the differential equation obtained by eliminating the arbitrary constant C in the equation representing the family of curves xy = C cos x.