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If I have a matrix in the form $Ax=B$, why must I have $beginbmatrixi\jendbmatrix=βbeginbmatrix-2\1endbmatrix?$

Why are $A=beginbmatrix a & b \ c & d endbmatrix$ and $B=beginbmatrix 0 & 1 \ -det(A) & operatornametr(A) endbmatrix$ similar?Solve $3X =beginbmatrix0&3\6&9endbmatrix$ for $X$The number of the solutions of $‎ x^10=‎ ‎ ‎beginbmatrix1&0\‎ ‎0&1‎ ‎endbmatrix‎$Given an eigen values evaluate $S*tinybeginbmatrix 0\1\0 endbmatrix$Interpreting $beginbmatrix 1 & 2 & 3 endbmatrix cdot h $ as a scalar or matrix multiplication$beginbmatrix6&a\b&1endbmatrixbeginbmatrix2\0endbmatrix=beginbmatrix4\-10endbmatrix$ Find $a$ and $b$Eigenvectors of $beginbmatrixa&-b\b&aendbmatrix$Is $beginbmatrix0&1\0&1endbmatrix$ linearly dependent?Find matrix $A$ of $Ax=b$ if $b=beginbmatrix 1 \ 2 \ 1 \ endbmatrix \$Finding all $3times3$ matrices such that $Abeginbmatrixx\y\zendbmatrix=beginbmatrix1\0\0endbmatrix$ has two distinct solutions

0

$begingroup$

I have inserted numbers in place of i and j, and have successfully deduced the value of β as a coefficient. However, i am unsure why we must have that equation if we know $Abeginbmatrixi\jendbmatrix=0$.

linear-algebra matrices

share|cite|improve this question

edited Mar 21 at 15:16

Thomas Andrews

131k12147298

asked Mar 21 at 15:02

MorpheusZionMorpheusZion

84

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This question is very unclear - it in not clear what your vectors have to do with $Ax=B.$ What do you mean "you must have?"
  $endgroup$
  – Thomas Andrews
  Mar 21 at 15:13
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If "$Abeginbmatrix i \ jendbmatrix= 0$" and "$Ax= B$" then $Aleft(x+ beta beginbmatrix i \ jendbmatrixright)= Ax+ beta Abeginbmatrix i \ j endbmatrix= B$ for any $beta$. Is that what you are asking?
  $endgroup$
  – user247327
  Mar 21 at 15:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes thank you, sorry for the poor wording
  $endgroup$
  – MorpheusZion
  Mar 21 at 23:37
  

  
  
  
  

add a comment | 

0

$begingroup$

I have inserted numbers in place of i and j, and have successfully deduced the value of β as a coefficient. However, i am unsure why we must have that equation if we know $Abeginbmatrixi\jendbmatrix=0$.

linear-algebra matrices

share|cite|improve this question

edited Mar 21 at 15:16

Thomas Andrews

131k12147298

asked Mar 21 at 15:02

MorpheusZionMorpheusZion

84

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  This question is very unclear - it in not clear what your vectors have to do with $Ax=B.$ What do you mean "you must have?"
  $endgroup$
  – Thomas Andrews
  Mar 21 at 15:13
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  If "$Abeginbmatrix i \ jendbmatrix= 0$" and "$Ax= B$" then $Aleft(x+ beta beginbmatrix i \ jendbmatrixright)= Ax+ beta Abeginbmatrix i \ j endbmatrix= B$ for any $beta$. Is that what you are asking?
  $endgroup$
  – user247327
  Mar 21 at 15:35
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes thank you, sorry for the poor wording
  $endgroup$
  – MorpheusZion
  Mar 21 at 23:37
  

  
  
  
  

add a comment | 

$begingroup$

I have inserted numbers in place of i and j, and have successfully deduced the value of β as a coefficient. However, i am unsure why we must have that equation if we know $Abeginbmatrixi\jendbmatrix=0$.

linear-algebra matrices

share|cite|improve this question

edited Mar 21 at 15:16

Thomas Andrews

131k12147298

asked Mar 21 at 15:02

MorpheusZionMorpheusZion

84

$endgroup$

share|cite|improve this question

edited Mar 21 at 15:16

Thomas Andrews

131k12147298

asked Mar 21 at 15:02

MorpheusZionMorpheusZion

84

share|cite|improve this question

edited Mar 21 at 15:16

Thomas Andrews

131k12147298

asked Mar 21 at 15:02

MorpheusZionMorpheusZion

84

edited Mar 21 at 15:16

Thomas Andrews

131k12147298

edited Mar 21 at 15:16

Thomas Andrews

131k12147298

asked Mar 21 at 15:02

MorpheusZionMorpheusZion

84

asked Mar 21 at 15:02

MorpheusZionMorpheusZion

84