Determine if the equation Ax = b is consistent for all possible b1 and b2 . If the equation is not consistent for all possible b1 and b2 , give a description of the set of all b for which the equation is consistent (i.e., the condition which must be satisfied by b1 and b2 )

Question

anonymous · Answer

1-The equation is consistent for all possible b1 and b2 .
2-The equation is consistent for all b1 and b2 satisfying b1 + b2 =0.    
3-The equation is consistent for all b1 and b2 satisfying b1 - 8b2 =0.
4-The equation is consistent for all b1 and b2 satisfying 8b1 - b2 =0.
5-None of the above.

anonymous · Answer

attachment

anonymous · Answer

@ganeshie8 could you please help me with this one?

anonymous · Answer

im not sure what i have to do to the matrix to work this out

anonymous · Answer

@sidsiddhartha  could you please help me with this one?

phi · Answer

you can show it is full rank by showing it has 2 pivots. (if that makes any sense)

ganeshie8 · Answer

Notice that the matrix has `two independent column vectors` - can you reach all the points in a `plane` using these two column vectors ?

ganeshie8 · Answer

|dw:1408195450752:dw|

anonymous · Answer

what do you mean by two independent column vectors?

ganeshie8 · Answer

they are pointing in different directions, so they're linearly independent column vectors :  you cannot get one vector from the other by scaling

anonymous · Answer

ohk!

anonymous · Answer

so no you cant reach all the points? using just those two vectors

ganeshie8 · Answer

why not ? tell me one point which you think you cannot reach using linear combinations of these two vectors

anonymous · Answer

oh using linear combination of these vectors i suppose u can

ganeshie8 · Answer

yes you can reach all the points by taking linear combinations of the columns of $A$,
that means the equation $Ax=b$ has solutions for all $b$

haseeb96 · Answer

$$\left[\begin{matrix}-8 & 8 \ 8 & 8\end{matrix}\right]\left(\begin{matrix}x \ y\end{matrix}\right)=\left(\begin{matrix}b1 \ b2\end{matrix}\right)$$

ganeshie8 · Answer

a fancy word for saying the same is $\text{consistent}$

haseeb96 · Answer

according  to yur condition 
Ax=b

anonymous · Answer

sorry nothing is showing up

anonymous · Answer

attachment

haseeb96 · Answer

$$\left[\begin{matrix}-8x+8y \ 8x+8y\end{matrix}\right] = \left(\begin{matrix}b1 \ b2\end{matrix}\right)$$

haseeb96 · Answer

but here it is showing 
just put x=IxI
                 IyI

haseeb96 · Answer

u just refresh yur page

haseeb96 · Answer

|dw:1408196642981:dw|
this is that thing which was written there .