Question

Write down the matrix a=[aij] where aij=jsin(ipi/4)

Answer 1

\[A=[aij] ->
aij=j \sin (\frac{ i \pi }{ 4 })\]

Answer 2

I have no idea how to do this so if you could show me

Answer 3

\[A=\left[\begin{matrix}a_{i,j}\end{matrix}\right], \text{ where }a_{i,j}=j\sin\left(\frac{i\pi}{4}\right)\]
Depending on the dimension of A, you'll have a matrix where any given element in row (i) and column (j) is of the form given (j sin(i pi/4)).
This means, for example, that the second row, third column is occupied by
\[a_{2,3}=3\sin\left(\frac{2\pi}{4}\right)=3\]
Suppose A is a 2x2 matrix. Then you have
\[\left[\begin{matrix}a_{1,1}&a_{1,2}\\a_{2,1}&a_{2,2}\end{matrix}\right]=\left[\begin{matrix}\sin\left(\frac{\pi}{4}\right)&2\sin\left(\frac{\pi}{4}\right)\\\sin\left(\frac{2\pi}{4}\right)&2\sin\left(\frac{2\pi}{4}\right)\end{matrix}\right]=\left[\begin{matrix}\frac{1}{\sqrt2}&\frac{2}{\sqrt2}\\1&2\end{matrix}\right]\]

Answer 4

Oh I must have missed notes on this stuff.Do you just assume that it is a 2x2 matrix?

Answer 5

Not necessarily, I just used that as an example.

Answer 6

Oh okay thanks!!