Question

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

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.

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

Write the value of λ so that the vectors $\stackrel{\rightarrow}{a}\$ = $2 \stackrel{\wedge}{i}+λ\stackrel{\wedge}{j} +\stackrel{\wedge}{k}$ and $\stackrel{\rightarrow}{b}\$ = $\stackrel{\wedge}{i}-2\stackrel{\wedge}{j} +3\stackrel{\wedge}{k}$ are perpendicular to each other ?

If A is square matrix of order 3 such that $|a d j A|=$ 64, find $|A|.$

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.

Find the differential equation representing the family of curves $V={\frac{A}{r}}+B,$ where A and B are arbitrary constants.