Question

Write the projection of $\stackrel{\rightarrow}{b}\$ +$\stackrel{\rightarrow}{c}\$ on $\stackrel{\rightarrow}{a}\$,where $\stackrel{\rightarrow}{a}\$ = $2\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$, $\stackrel{\rightarrow}{b}\$ = $\stackrel{\wedge}{i}+2\stackrel{\wedge}{j} -2\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{c}\$ = $2\stackrel{\wedge}{i}-\stackrel{\wedge}{j} +4\stackrel{\wedge}{k}$

If A is a square matrix and | A | = 2, then write the value of | AA’ |, where A’ is the transpose of matrix A.

Let A and B are matrices of order 3 x 2 and 2 x 4 respectively. Write the order of matrix (AB).

Write the degree of the differential equation : $\left(\frac{d y}{d x}\right)^{4}+3x\frac{d^{2}y}{d x^{2}}=0.$

Find the value of x + y from the following equation : 2 $\left(\begin{array}{l l }x & 5 \\ 7 & y-3\end{array}\right)$ + $\left(\begin{array}{l l }3 & -4 \\ 1 & 2\end{array}\right)$ = $\left(\begin{array}{l l }7 & 6 \\ 15 & 14\end{array}\right)$ .

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

Solve the following matrix equation for x : [x 1] $\left(\begin{array}{l l }1 & 0 \\ -2 & 0\end{array}\right)$ = 0.