Question

If A = $\left(\begin{array}{l l l }1 & 2 & 2 \\ 2 & 1 & x \\ -2 & 2 & -1\end{array}\right)$ is a matrix satisfying AA’ = 9I, find x.

Find the sum of the vectors : $\stackrel{\rightarrow}{a}=\stackrel{\wedge}{i}-2\stackrel{\wedge}{j},$ $\vec{b}=2\hat{i}-3\hat{j},$ $\vec{c}=2\hat{i}+3\hat{k},$

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

What is the degree of the following differential equation ? $5x\biggl(\frac{d y}{d x}\biggr)^{2}-\frac{d^{2}y}{d x^{2}}-6y\;=\log x.$

Give an example of a skew symmetric matrix of order 3.

If matrix A = [1 2 3], then write AA’.

If matrix A = $\left(\begin{array}{l l }3 & -3 \\ -3 & 3\end{array}\right)$ and A² = λA, then write the value of λ.