if
[ -4 5
-2 5/2]

find a non-zero 2 by 2 zero matrix X, such that A.X=O_2x2

Question

if
[ -4 5
  -2 5/2]

find a non-zero 2 by 2 zero matrix X, such that  A.X=O_2x2

amistre64 · Answer

is O spose to be anything special?  other than a 2x2 matrix?

amistre64 · Answer

and I take it the given matrix is A:

anonymous · Answer

$$\left[\begin{matrix}-4 & 5 \ -2 & 5/2\end{matrix}\right]$$

amistre64 · Answer

find a nonzero, zero matrix?

amistre64 · Answer

A.X = 0  is what i think im reading, such that X is not a 0

amistre64 · Answer

so they need to be orthogonal at best

amistre64 · Answer

$$z_{11}=-4x_{11}+5x_{21}=0$$
$$z_{21}=-2x_{11}+\frac{5}{2}x_{21}=0$$
$$z_{12}=-4x_{12}+5x_{22}=0$$
$$z_{22}=-2x_{12}+\frac{5}{2}_{22}=0$$
would be our corresponding equations

maybe

anonymous · Answer

A.X= to the letter O and not 0

amistre64 · Answer

the name is unimportant methinks, but its spose to zero out

amistre64 · Answer

-4x + 5y = 0
  4x - 5y = 0
-----------
  i dont thinks its doable

but i could be wrong

amistre64 · Answer

detA = 0 so its dependant for starters, i think that throws a monkeywrench in the plans

amistre64 · Answer

or maybe, since its just one vector, we can flip and negate the entries to get a perp vector; hmmm

$$\begin{pmatrix}-4&5\-2&\frac{5}{2}\end{pmatrix}.\begin{pmatrix}2&-\frac{5}{2}\-4&5\end{pmatrix}$$
maybe?

amistre64 · Answer

that doesnt work either

amistre64 · Answer

i was on the right track :)

amistre64 · Answer

http://www.wolframalpha.com/input/?i=%7B%7B-4%2C5%7D%2C%7B-2%2C5%2F2%7D%7D.%7B%7B-5%2C-5%2F2%7D%2C%7B-4%2C-2%7D%7D this one!! lol