Find the determinant of the matrix.

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
2
down vote

favorite
3












If
$textdetleft[beginmatrixa & 1 & c\
b & 1 & d\
e& 1 & f
endmatrixright]= -3$
and $textdetleft[beginmatrixa & 1 & c\
b & 2 & d\
e& 3 & f
endmatrixright]= 5$
find
$textdetleft[beginmatrixa & -4 & c\
b & -7 & d\
e& -10 & f
endmatrixright]$.



How do I approach this? The section deals with the effect of row operations on the determinate.






linear-algebra determinant







share|cite|improve this question

























    up vote
    2
    down vote

    favorite
    3












    If
    $textdetleft[beginmatrixa & 1 & c\
    b & 1 & d\
    e& 1 & f
    endmatrixright]= -3$
    and $textdetleft[beginmatrixa & 1 & c\
    b & 2 & d\
    e& 3 & f
    endmatrixright]= 5$
    find
    $textdetleft[beginmatrixa & -4 & c\
    b & -7 & d\
    e& -10 & f
    endmatrixright]$    .



    How do I approach this? The section deals with the effect of row operations on the determinate.






    linear-algebra determinant







    share|cite|improve this question























      up vote
      2
      down vote

      favorite
      3









      up vote
      2
      down vote

      favorite
      3






      3





      If
      $textdetleft[beginmatrixa & 1 & c\
      b & 1 & d\
      e& 1 & f
      endmatrixright]= -3$
      and $textdetleft[beginmatrixa & 1 & c\
      b & 2 & d\
      e& 3 & f
      endmatrixright]= 5$
      find
      $textdetleft[beginmatrixa & -4 & c\
      b & -7 & d\
      e& -10 & f
      endmatrixright]$      .



      How do I approach this? The section deals with the effect of row operations on the determinate.






      linear-algebra determinant







      share|cite|improve this question













      If
      $textdetleft[beginmatrixa & 1 & c\
      b & 1 & d\
      e& 1 & f
      endmatrixright]= -3$
      and $textdetleft[beginmatrixa & 1 & c\
      b & 2 & d\
      e& 3 & f
      endmatrixright]= 5$
      find
      $textdetleft[beginmatrixa & -4 & c\
      b & -7 & d\
      e& -10 & f
      endmatrixright]$      .



      How do I approach this? The section deals with the effect of row operations on the determinate.






      linear-algebra determinant




      linear-algebra determinant






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked 2 hours ago









      johnny133253

      1479




      1479




















          1 Answer
          1






          active

          oldest

          votes

















          up vote
          3
          down vote



          accepted










          The determinant is linear in every row and in every column. Thus, this problem is equivalent to finding $φ(-4,-7,-10)$ for a linear map $φ colon ℚ^3 → ℚ$ with $φ(1,1,1) = -3$ and $φ(1,2,3)= 5$. Do you see that – what is $φ$ here? Can you solve this reduced problem?






          share|cite|improve this answer




















          • Makes perfect sense. Thanks. I just need to solve a system of equations.
            – johnny133253
            1 hour ago







          • 1




            @johnny133253 Yeah, or you just guess the linear combination $(-4,-7,-10) = μ(1,1,1) + λ(1,2,3)$.
            – k.stm
            1 hour ago










          • Yup, so $mu = -1$ and $lambda = -3$. Much appreciated.
            – johnny133253
            1 hour ago










          • @johnny133253,so have you got the value of determinant asked?
            – Dhamnekar Winod
            52 mins ago










          • Yes its $(-1)(-3) + (-3)(5) = -12$
            – johnny133253
            51 mins ago










          Your Answer




          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "69"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          convertImagesToLinks: true,
          noModals: false,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );













           

          draft saved


          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2975577%2ffind-the-determinant-of-the-matrix%23new-answer', 'question_page');

          );

          Post as a guest

















          1 Answer
          1






          active

          oldest

          votes








          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          3
          down vote



          accepted










          The determinant is linear in every row and in every column. Thus, this problem is equivalent to finding $φ(-4,-7,-10)$ for a linear map $φ colon ℚ^3 → ℚ$ with $φ(1,1,1) = -3$ and $φ(1,2,3)= 5$. Do you see that – what is $φ$ here? Can you solve this reduced problem?






          share|cite|improve this answer




















          • Makes perfect sense. Thanks. I just need to solve a system of equations.
            – johnny133253
            1 hour ago







          • 1




            @johnny133253 Yeah, or you just guess the linear combination $(-4,-7,-10) = μ(1,1,1) + λ(1,2,3)$.
            – k.stm
            1 hour ago










          • Yup, so $mu = -1$ and $lambda = -3$. Much appreciated.
            – johnny133253
            1 hour ago










          • @johnny133253,so have you got the value of determinant asked?
            – Dhamnekar Winod
            52 mins ago










          • Yes its $(-1)(-3) + (-3)(5) = -12$
            – johnny133253
            51 mins ago














          up vote
          3
          down vote



          accepted










          The determinant is linear in every row and in every column. Thus, this problem is equivalent to finding $φ(-4,-7,-10)$ for a linear map $φ colon ℚ^3 → ℚ$ with $φ(1,1,1) = -3$ and $φ(1,2,3)= 5$. Do you see that – what is $φ$ here? Can you solve this reduced problem?






          share|cite|improve this answer




















          • Makes perfect sense. Thanks. I just need to solve a system of equations.
            – johnny133253
            1 hour ago







          • 1




            @johnny133253 Yeah, or you just guess the linear combination $(-4,-7,-10) = μ(1,1,1) + λ(1,2,3)$.
            – k.stm
            1 hour ago










          • Yup, so $mu = -1$ and $lambda = -3$. Much appreciated.
            – johnny133253
            1 hour ago










          • @johnny133253,so have you got the value of determinant asked?
            – Dhamnekar Winod
            52 mins ago










          • Yes its $(-1)(-3) + (-3)(5) = -12$
            – johnny133253
            51 mins ago












          up vote
          3
          down vote



          accepted







          up vote
          3
          down vote



          accepted






          The determinant is linear in every row and in every column. Thus, this problem is equivalent to finding $φ(-4,-7,-10)$ for a linear map $φ colon ℚ^3 → ℚ$ with $φ(1,1,1) = -3$ and $φ(1,2,3)= 5$. Do you see that – what is $φ$ here? Can you solve this reduced problem?






          share|cite|improve this answer












          The determinant is linear in every row and in every column. Thus, this problem is equivalent to finding $φ(-4,-7,-10)$ for a linear map $φ colon ℚ^3 → ℚ$ with $φ(1,1,1) = -3$ and $φ(1,2,3)= 5$. Do you see that – what is $φ$ here? Can you solve this reduced problem?







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 2 hours ago









          k.stm

          10.6k22249




          10.6k22249











          • Makes perfect sense. Thanks. I just need to solve a system of equations.
            – johnny133253
            1 hour ago







          • 1




            @johnny133253 Yeah, or you just guess the linear combination $(-4,-7,-10) = μ(1,1,1) + λ(1,2,3)$.
            – k.stm
            1 hour ago










          • Yup, so $mu = -1$ and $lambda = -3$. Much appreciated.
            – johnny133253
            1 hour ago










          • @johnny133253,so have you got the value of determinant asked?
            – Dhamnekar Winod
            52 mins ago










          • Yes its $(-1)(-3) + (-3)(5) = -12$
            – johnny133253
            51 mins ago
















          • Makes perfect sense. Thanks. I just need to solve a system of equations.
            – johnny133253
            1 hour ago







          • 1




            @johnny133253 Yeah, or you just guess the linear combination $(-4,-7,-10) = μ(1,1,1) + λ(1,2,3)$.
            – k.stm
            1 hour ago










          • Yup, so $mu = -1$ and $lambda = -3$. Much appreciated.
            – johnny133253
            1 hour ago










          • @johnny133253,so have you got the value of determinant asked?
            – Dhamnekar Winod
            52 mins ago










          • Yes its $(-1)(-3) + (-3)(5) = -12$
            – johnny133253
            51 mins ago















          Makes perfect sense. Thanks. I just need to solve a system of equations.
          – johnny133253
          1 hour ago





          Makes perfect sense. Thanks. I just need to solve a system of equations.
          – johnny133253
          1 hour ago





          1




          1




          @johnny133253 Yeah, or you just guess the linear combination $(-4,-7,-10) = μ(1,1,1) + λ(1,2,3)$.
          – k.stm
          1 hour ago




          @johnny133253 Yeah, or you just guess the linear combination $(-4,-7,-10) = μ(1,1,1) + λ(1,2,3)$.
          – k.stm
          1 hour ago












          Yup, so $mu = -1$ and $lambda = -3$. Much appreciated.
          – johnny133253
          1 hour ago




          Yup, so $mu = -1$ and $lambda = -3$. Much appreciated.
          – johnny133253
          1 hour ago












          @johnny133253,so have you got the value of determinant asked?
          – Dhamnekar Winod
          52 mins ago




          @johnny133253,so have you got the value of determinant asked?
          – Dhamnekar Winod
          52 mins ago












          Yes its $(-1)(-3) + (-3)(5) = -12$
          – johnny133253
          51 mins ago




          Yes its $(-1)(-3) + (-3)(5) = -12$
          – johnny133253
          51 mins ago

















           

          draft saved


          draft discarded















































           


          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2975577%2ffind-the-determinant-of-the-matrix%23new-answer', 'question_page');

          );

          Post as a guest
































































          Comments

          Post a Comment

          Popular posts from this blog

          What does second last employer means? [closed]

          Image
          Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote -3 down vote favorite Say, for example I have worked in the following companies, Company A => 2010 - 2011 Company B => 2011 - 2012 Company C => 2012 - Till Date Company D => Have offer Now assume Company D is asking to submit documents from my second last employer. So from the list of companies given, which company would be qualified as second last employer? software-industry employer share | improve this question asked Aug 10 '14 at 5:16 Rajaprabhu Aravindasamy 559 1 6 13 closed as off-topic by Jim G., jmort253 ♦ Aug 11 '14 at 1:58 This question appears to be off-topic. The users who voted to close gave this specific reason: "Questions seeking advice on company-specific regulations, agreements, or policies should be directed to your manager or HR department. Questions that address...
          Read more

          Installing NextGIS Connect into QGIS 3?

          Image
          Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote 1 down vote favorite Just acquired free version of NEXTGIS and trying to install the plugin for QGIS. It tells me it was not designed for version 3 of QGIS. How do I set up the QGIS-NEXTGIS interface then? qgis qgis-plugins nextgis share | improve this question edited 3 hours ago PolyGeo ♦ 51.9k 17 77 233 asked 4 hours ago IanGS 16 4 New contributor IanGS is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct. add a comment  |  up vote 1 down vote favorite Just acquired free version of NEXTGIS and trying to install the plugin for QGIS. It tells me it was not designed for version 3 of QGIS. How do I set up the QGIS-NEXTGIS interface then? qgis qgis-plugin...
          Read more

          One-line joke

          A one-liner is a joke that is delivered in a single line. A good one-liner is said to be pithy - concise and meaningful. [1] Comedians and actors use this comedic method as part of their act, e.g. Jimmy Carr, Tommy Cooper, Rodney Dangerfield, Norm Macdonald, Ken Dodd, Stewart Francis, Zach Galifianakis, Mitch Hedberg, Anthony Jeselnik, Milton Jones, Shappi Khorsandi, Jay London, Mark Linn-Baker, Demetri Martin, Groucho Marx, Dan Mintz, Emo Philips, Tim Vine, Steven Wright and Henny Youngman and Arnold Schwarzenegger. [ citation needed ] Many fictional characters are also known to deliver one-liners, including James Bond, who usually includes pithy and laconic quips after disposing of a villain. [ citation needed ] Examples "A baby seal walks into a club." "A dyslexic man walks into a bra." (Anonymous) "There are three types of people, those who can count and those who can't." "Venison's dear, isn't it?" (Jimmy Carr) "An escala...
          Read more