## anonymous 5 years ago if [ -4 5 -2 5/2] find a non-zero 2 by 2 zero matrix X, such that A.X=O_2x2

1. amistre64

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

2. amistre64

and I take it the given matrix is A:

3. anonymous

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

4. amistre64

find a nonzero, zero matrix?

5. amistre64

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

6. amistre64

so they need to be orthogonal at best

7. amistre64

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

8. anonymous

A.X= to the letter O and not 0

9. amistre64

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

10. amistre64

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

11. amistre64

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

12. amistre64

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?

13. amistre64

that doesnt work either

14. amistre64

i was on the right track :)

15. amistre64

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