determinant isn't a linear form}}$, so I can't figure out how to end the proof.
What would be the next step? Thank you in advance!

A:

In general, given a matrix $B\in M_{n}$ whose columns are $(v_{1},...,v_{n})$, we have that the product $AB$ is the matrix whose columns are $(Av_{1},...,Av_{n})$. 
$\Rightarrow$ Assume $\lambda\in\sigma(A)$. Let $v$ be a non-zero eigenvector of $A$ corresponding to $\lambda$. Consider the matrix $B$ whose columns are $(v,\overset{\rightarrow}{0},\overset{\rightarrow}{0},...,\overset{\rightarrow}{0})$. Then, $\text{Λ}_{A}(B)=AB$ is the matrix whose columns are $(Av,\overset{\rightarrow}{0},\overset{\rightarrow}{0},...,\overset{\rightarrow}{0})$, i.e., it is $\lambda B$.
$\Leftarrow$ Assume $\lambda\in\sigma(\text{Λ}_{A})$. Let $B$ be a non-zero eigenvector of $\text{Λ}_{A}$ corresponding to $\lambda$. Let $v$ be a non-zero column of $B$. Then, $Av=\lambda v$, so that $\lambda\in\sigma(A)$. 

 Q:

Unable to click on graph with lower values to see data in CRM 2015

I have graph created in CRM as seen in the picture below. I am unable to click and view data for bars with lower values ( For ex: I am unable to click on values 1s, 2s and 14 whereas I am able to click and view data for bigger values ) 
Also I am able to click and see data for lower values in Stack graph not in bar graph.
** It doesn't matter the territory holder or quarter, its for all the values below 15.  
Is there anything I can do, to be able to click  and view data related to bars with lower values?
CRM Graph
Thank you!

A:

I would guess that those columns are just simply too small. You could play with the xml of your chart and add some scale breaks. It should make those columns bigger and available for clicking.
Have a look here to learn about scale breaks: https://crmchartguy.wordpress.com/category/scalebreak
determinant isn't a linear form}}$, so I can't figure out how to end the proof. 
 What would be the next gradation? Thank you in overture! 

 A: 

 In general, given a matrix $ B\in M_{n}$ whose column are $ (v_{1},... ,v_{n})$, we have that the product $ AB$ is the matrix whose column are $ (Av_{1},... ,Av_{n})$. 
 $ \Rightarrow$ Assume $ \lambda\in\sigma(A)$. Let $ v$ be a non - zero eigenvector of $ A$ corresponding to $ \lambda$. see the matrix $ B$ whose columns are $ (v,\overset{\rightarrow}{0},\overset{\rightarrow}{0},... ,\overset{\rightarrow}{0})$. Then, $ \text{Λ}_{A}(B)=AB$ is the matrix whose columns are $ (Av,\overset{\rightarrow}{0},\overset{\rightarrow}{0},... ,\overset{\rightarrow}{0})$, i.e., it is $ \lambda B$. 
 $ \Leftarrow$ Assume $ \lambda\in\sigma(\text{Λ}_{A})$. lease $ B$ be a non - zero eigenvector of $ \text{Λ}_{A}$ corresponding to $ \lambda$. Let $ v$ be a non - zero column of $ B$. Then, $ Av=\lambda v$, so that $ \lambda\in\sigma(A)$. 

  Q: 

 ineffective to click on graph with lower value to see data in CRM 2015 

 I have graph make in CRM as seen in the picture below. I am ineffective to click and view datum for bars with low values (For ex: I am unable to click on values 1s, 2s and 14 whereas I am able to snap and view data for bigger values) 
 Also I am able to click and see data for lower values in Stack graph not in bar graph. 
 * * It doesn't matter the territory holder or quarter, its for all the values below 15.  
 Is there anything I can do, to be able to click   and see data related to bar with low values? 
 CRM Graph 
 Thank you! 

 A: 

 I would guess that those columns are barely simply too small. You could play with the xml of your chart and lend some scale breaks. It should make those columns bigger and available for clicking. 
 get a look here to learn about scale breaks: https://crmchartguy.wordpress.com/category/scalebreak
detfrminant isn't a linear furm}}$, so I can't fnture ont how fo end tfe proof.
What would be the neet srep? Tyank you in advance!

A:

In general, hiven a natrmx $B\in M_{n}$ whose rklumns are $(v_{1},...,v_{h})$, we kate that the procuct $AB$ is the matrix whmsd eolumns are $(Av_{1},...,Av_{n})$. 
$\Rightarrow$ Assume $\jambda\im\slgma(A)$. Let $v$ be a npg-zerk eigenvector of $A$ corresponding tk $\lambde$. Consider the katrix $B$ whose columns are $(v,\ovfrset{\rightarrow}{0},\ovegset{\rightartkw}{0},...,\odwrset{\rightarfow}{0})$. Then, $\ttxc{Λ}_{A}(B)=AB$ is thg matrix whose columns are $(Av,\ovefset{\rnghtarrow}{0},\ovgxwet{\ghghtarrow}{0},...,\ovxrset{\rpghtarrow}{0})$, i.e., ln is $\lakbda B$.
$\Lrftarrow$ Assumc $\lamuda\ib\sigma(\text{Λ}_{A})$. Let $B$ be e non-zero eigenvectot of $\text{Λ}_{A}$ ckrresponding to $\lqmvda$. Lgt $v$ te a bon-xerk rolhmn of $B$. Vhen, $Av=\lambsa v$, so thar $\lambda\in\sigma(A)$. 

 Q:

Inwvle to click kn gra[h with lower values to see data in CRM 2015

I habe graph created in CRM as seen in the pictute below. I am unable to click and view data for bars with lmwer tauuew ( Wir ex: I am unable to click on values 1s, 2s and 14 wrsrtas I am able to glick and view dats vot bigger valuer ) 
Also I am able to click wnd see data for lowew vakues in Stack graph not in var graph.
** It eoesn't matter the cerritory houder or qiarter, its for all the ralues below 15.  
Is there angghing I can do, tu bv abne to click  and view data related vo baxs with uowet valuef?
CRM Graph
Hhank you!

A:

I would guess hhat jhose wolumns arf just simply too small. You could play with tne xmn of youx charb and add some fcale breaks. Ij should iake ghose colujns bigjer and avaijable for cliwning.
Have a lmok here to oearb about rcale breaks: hytps://crmchcxtguy.wordpress.com/category/scelebtezk
determinant isn't a linear form}}$, so I out to end proof. What would you advance! A: In given a matrix M_{n}$ whose columns are $(v_{1},...,v_{n})$, we that the product $AB$ is the matrix whose columns are $(Av_{1},...,Av_{n})$. $\Rightarrow$ Assume Let $v$ be a non-zero eigenvector of $A$ corresponding to $\lambda$. Consider the $B$ columns $(v,\overset{\rightarrow}{0},\overset{\rightarrow}{0},...,\overset{\rightarrow}{0})$. $\text{Λ}_{A}(B)=AB$ is the matrix whose columns are $(Av,\overset{\rightarrow}{0},\overset{\rightarrow}{0},...,\overset{\rightarrow}{0})$, i.e., it is $\lambda B$. $\Leftarrow$ Assume $\lambda\in\sigma(\text{Λ}_{A})$. $B$ be a non-zero eigenvector of $\text{Λ}_{A}$ corresponding $\lambda$. Let $v$ be non-zero column of $B$. Then, v$, that $\lambda\in\sigma(A)$. Unable click graph with lower to see data in CRM 2015 I have graph created in CRM as seen in the picture I am click and data bars lower values ( I am unable to click on and 14 whereas I am able to click view data bigger values ) Also I am to click and see data for lower values Stack graph not in bar graph. ** It doesn't matter the territory holder or quarter, all the values below Is there anything can to able click and data related to bars with lower values? CRM Graph Thank you! I would guess that those columns are just simply too could with the xml your chart and add scale It should make those and for look to about scale breaks: https://crmchartguy.wordpress.com/category/scalebreak
determinant isn't a linear forM}}$, so I can't fiGure oUt hOw tO eNd thE proOf.
What would be tHE nexT step? Thank you in advance!

a:

In geNeRAl, giVEn A matrIx $B\in M_{n}$ WHoSE ColUmNs Are $(V_{1},...,v_{N})$, We Have tHat The prodUct $AB$ is the MatRiX whose columnS ArE $(Av_{1},...,Av_{n})$. 
$\RighTarRow$ Assume $\lamBda\In\sigmA(A)$. let $V$ Be a noN-zeRo eigEnvectOR of $A$ coRrespondiNg TO $\lambdA$. consideR THe MatrIx $B$ whose columns arE $(V,\oVErset{\rightarroW}{0},\oversEt{\RIgHTArrOw}{0},...,\oVerset{\righTaRrow}{0})$. THEn, $\text{Λ}_{a}(b)=Ab$ IS The MAtrix whose colUmns are $(Av,\ovERseT{\rightArRow}{0},\OVerset{\RightArROw}{0},...,\oVerset{\rightArroW}{0})$, i.e., it is $\laMbda B$.
$\LEFtarrow$ aSsume $\laMbda\in\SigMa(\tExt{Λ}_{a})$. leT $B$ Be a NoN-ZerO EiGenVEctOr of $\text{λ}_{A}$ CoRrespOndiNG TO $\LambDa$. LEt $v$ bE a non-Zero column of $B$. theN, $Av=\lAMbdA v$, so tHat $\laMbda\In\Sigma(a)$. 

 Q:

UnabLe to cLiCk on graph with loWer vAlues to seE daTa In CrM 2015

i have GRaph crEatEd iN CRM as sEen in thE PicTuRE BElOw. I am unable to click AnD VIeW data for Bars wiTH lOwER values ( FOr Ex: I Am unABLe to cLick ON vAlues 1s, 2s aNd 14 wherEAs i aM able to ClIck and ViEw dAta For biGGer vAlues ) 
ALso I am abLe to cLIck and see data fOR lower values iN stACK gRAph nOt iN bar graph.
** It DoesN'T matTer tHE tErrITory hOlder Or QUaRTer, its for all the valuEs Below 15.  
IS therE anything I can Do, to be able TO CLick  and vIew dATa RElated to bars wiTh lowEr values?
CRm graph
ThaNk you!

a:

I would gUess that tHOSe columnS arE juSt sImpLY ToO small. You coulD PLay wItH the xml Of yOur charT anD adD soMe sCaLe breaks. IT should mAkE tHoSe ColUmns bIGger and aVaIlaBlE foR clicKIng.
HavE a looK herE tO lEArn About scALe BREaks: HtTpS://crmChaRtGuy.woRdprESs.cOm/categOry/scalebReaK
determinant isn't a linear  form}}$,so Ican 'tfi gure  out  how to end th e  pro of.
What would be thenextst e p? T h an k you  in adv a nc e ! 

A :
I n g en e ra l, gi ven  a matr ix $B\in M _{n }$  whose colum n sare $(v_{1 },. ..,v_{n})$,wehave t ha t t h e pro duc t $AB $ is t h e matr ix whoseco l umns a r e $(Av_ { 1 }, ..., Av_{n})$. 
$\Righ t ar r ow$ Assume $\l ambda\ in \ si g m a(A )$.  Let $v$ b ea non - zero ei g en v e c tor of $A$ corres ponding to$ \la mbda$.  C ons i der th e mat ri x  $B $ whose col umns  are $(v, \overs e t{\righ t arrow}{ 0},\ov ers et{ \rig h ta rr ow} {0 } ,.. . ,\ ove r set {\righta rr ow }{0}) $. T h e n ,  $\t ext {Λ}_ {A}(B )=AB$ is themat rixw hos e col umnsare$( Av,\o verset {\rig ht arrow}{0},\over set{ \rightarr ow} {0 },. .. ,\ove r set{\r igh tar row}{0} )$, i.e . , i ti s $\ lambda B$.
$\Lefta rr o w $Assume $ \lambd a \i n\ s igma(\te xt {Λ} _{A} ) $ . Let  $B$ be  a non-z ero ei g en ve ctor of  $ \text{ Λ} _{A }$corre s pond ing to  $\lambd a$. L e t $v$ be a non - zero column o f  $ B $ .T hen,  $A v=\lambda v $, s o  tha t $\ l am bda \ in\si gma(A )$ .   Q:

Unable to clic kon gra ph wi th lower valu es to seed a t a in CRM  201 5 
I  have graph cr eated  in CRM as seen inthe p icture b elow. I a m unable t o c lic k a ndv i ew  data for bar s with  l ower va lue s ( For  ex : I  am  un ab le to cli ck on va lu es  1 s,  2s  and1 4 wherea sI a mabl e toc lick a nd vi ew d at af orbiggerv al u e s )
A ls o Iamab le to  cli c k a nd seedata forlow e r va lu es  in Sta ck graph notin  bar graph .**It doe s n 't matte r the territory holdero r quart er,  itsforall the v alu es bel ow1 5.  
I s ther e any th ing I  cand o ,tobe  able to c l i ck andvi ew d ata rel ated to bars withl owe r values?
CRM  Gr aphT h an k y o u! 
A: 
I  wo u l d guess that th ose column sa re  just simp l y t oo  small.  You co uld p l ay with  the xmlof your c ha rt a n d  ad d some sca le break s. It sho u ld ma k ethose  co lumnsbi gge r and  avail a ble  forclicki ng .
Have  a lo ok  here to  learn about scale brea ks: ht tps:/ /cr mchartguy .wo r dpr ess.com/c ateg ory/scaleb rea k
determinant isn't_a linear_form}}$, so I can't_figure out_how_to end_the_proof.
What would be_the next step?_Thank you in advance!

A:

In_general, given a_matrix_$B\in M_{n}$ whose columns are $(v_{1},...,v_{n})$, we have that the product $AB$ is the_matrix_whose columns_are_$(Av_{1},...,Av_{n})$._
$\Rightarrow$ Assume $\lambda\in\sigma(A)$. Let $v$_be a non-zero eigenvector of_$A$ corresponding_to $\lambda$. Consider the matrix $B$ whose columns_are_$(v,\overset{\rightarrow}{0},\overset{\rightarrow}{0},...,\overset{\rightarrow}{0})$. Then, $\text{Λ}_{A}(B)=AB$_is the matrix whose columns are $(Av,\overset{\rightarrow}{0},\overset{\rightarrow}{0},...,\overset{\rightarrow}{0})$, i.e., it_is $\lambda B$.
$\Leftarrow$ Assume $\lambda\in\sigma(\text{Λ}_{A})$. Let_$B$ be a_non-zero_eigenvector_of $\text{Λ}_{A}$ corresponding to_$\lambda$. Let $v$ be a non-zero_column of $B$. Then, $Av=\lambda v$,_so that $\lambda\in\sigma(A)$. 

 Q:

Unable to click_on graph with lower values to_see data in CRM 2015

I_have graph_created in CRM as seen_in the picture_below. I_am unable to_click and view data for bars_with lower values_( For ex: I am unable_to_click on values_1s,_2s_and 14_whereas I am_able_to click_and_view data for bigger values )_
Also_I am able to click and see_data for lower values_in_Stack graph not in_bar graph.
** It doesn't matter_the territory holder or quarter, its_for all_the values_below 15.  
Is there anything I can do, to be_able to click  and view_data related to bars_with lower_values?
CRM_Graph
Thank you!

A:

I would_guess_that those_columns are just simply too small. You_could play_with the xml of your chart_and add some scale_breaks._It should make those columns bigger_and available for clicking.
Have a look_here to learn about scale_breaks:_https://crmchartguy.wordpress.com/category/scalebreak