Simultaneous Equations with Complex Coefficients Create a subroutine csimu1 to solve for the unknowns in a system of simultaneous linear equations that have complex coefficients. Test your subroutine by solving the system of equations shown below: (-2+5 (2024)

`); let searchUrl = `/search/`; history.forEach((elem) => { prevsearch.find('#prevsearch-options').append(`

${elem}

`); }); } $('#search-pretype-options').empty(); $('#search-pretype-options').append(prevsearch); let prevbooks = $(false); [ {title:"Recently Opened Textbooks", books:previous_books}, {title:"Recommended Textbooks", books:recommended_books} ].forEach((book_segment) => { if (Array.isArray(book_segment.books) && book_segment.books.length>0 && nsegments<2) { nsegments+=1; prevbooks = $(`

  • ${book_segment.title}
  • `); let searchUrl = "/books/xxx/"; book_segment.books.forEach((elem) => { prevbooks.find('#prevbooks-options'+nsegments.toString()).append(`

    ${elem.title} ${ordinal(elem.edition)} ${elem.author}

    `); }); } $('#search-pretype-options').append(prevbooks); }); } function anon_pretype() { let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_ANON')); }catch(e) {} if ('previous_books' in prebooks && 'recommended_books' in prebooks) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (typeof PREVBOOKS !== 'undefined' && Array.isArray(PREVBOOKS)) { new_prevbooks = PREVBOOKS; previous_books.forEach(elem => { for (let i = 0; i < new_prevbooks.length; i++) { if (elem.id == new_prevbooks[i].id) { return; } } new_prevbooks.push(elem); }); new_prevbooks = new_prevbooks.slice(0,3); previous_books = new_prevbooks; } if (typeof RECBOOKS !== 'undefined' && Array.isArray(RECBOOKS)) { new_recbooks = RECBOOKS; for (let j = 0; j < new_recbooks.length; j++) { new_recbooks[j].viewed_at = new Date(); } let insert = true; for (let i=0; i < recommended_books.length; i++){ for (let j = 0; j < new_recbooks.length; j++) { if (recommended_books[i].id == new_recbooks[j].id) { insert = false; } } if (insert){ new_recbooks.push(recommended_books[i]); } } new_recbooks.sort((a,b)=>{ adate = new Date(2000, 0, 1); bdate = new Date(2000, 0, 1); if ('viewed_at' in a) {adate = new Date(a.viewed_at);} if ('viewed_at' in b) {bdate = new Date(b.viewed_at);} // 100000000: instead of just erasing the suggestions from previous week, // we just move them to the back of the queue acurweek = ((new Date()).getDate()-adate.getDate()>7)?0:100000000; bcurweek = ((new Date()).getDate()-bdate.getDate()>7)?0:100000000; aviews = 0; bviews = 0; if ('views' in a) {aviews = acurweek+a.views;} if ('views' in b) {bviews = bcurweek+b.views;} return bviews - aviews; }); new_recbooks = new_recbooks.slice(0,3); recommended_books = new_recbooks; } localStorage.setItem('PRETYPE_BOOKS_ANON', JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books })); build_popup(); } } var whiletyping_search_object = null; var whiletyping_search = { books: [], curriculum: [], topics: [] } var single_whiletyping_ajax_promise = null; var whiletyping_database_initial_burst = 0; //number of consecutive calls, after 3 we start the 1 per 5 min calls function get_whiletyping_database() { //gets the database from the server. // 1. by validating against a local database value we confirm that the framework is working and // reduce the ammount of continuous calls produced by errors to 1 per 5 minutes. return localforage.getItem('whiletyping_last_attempt').then(function(value) { if ( value==null || (new Date()) - (new Date(value)) > 1000*60*5 || (whiletyping_database_initial_burst < 3) ) { localforage.setItem('whiletyping_last_attempt', (new Date()).getTime()); // 2. Make an ajax call to the server and get the search database. let databaseUrl = `/search/whiletype_database/`; let resp = single_whiletyping_ajax_promise; if (resp === null) { whiletyping_database_initial_burst = whiletyping_database_initial_burst + 1; single_whiletyping_ajax_promise = resp = new Promise((resolve, reject) => { $.ajax({ url: databaseUrl, type: 'POST', data:{csrfmiddlewaretoken: "VZtGjycQuWtbnkaVgeN2J925moMjqBotS1zhJtOf3yhxncAVrekiux1grEQdoJqI"}, success: function (data) { // 3. verify that the elements of the database exist and are arrays if ( ('books' in data) && ('curriculum' in data) && ('topics' in data) && Array.isArray(data.books) && Array.isArray(data.curriculum) && Array.isArray(data.topics)) { localforage.setItem('whiletyping_last_success', (new Date()).getTime()); localforage.setItem('whiletyping_database', data); resolve(data); } }, error: function (error) { console.log(error); resolve(null); }, complete: function (data) { single_whiletyping_ajax_promise = null; } }) }); } return resp; } return Promise.resolve(null); }).catch(function(err) { console.log(err); return Promise.resolve(null); }); } function get_whiletyping_search_object() { // gets the fuse objects that will be in charge of the search if (whiletyping_search_object){ return Promise.resolve(whiletyping_search_object); } database_promise = localforage.getItem('whiletyping_database').then(function(database) { return localforage.getItem('whiletyping_last_success').then(function(last_success) { if (database==null || (new Date()) - (new Date(last_success)) > 1000*60*60*24*30 || (new Date('2023-04-25T00:00:00')) - (new Date(last_success)) > 0) { // New database update return get_whiletyping_database().then(function(new_database) { if (new_database) { database = new_database; } return database; }); } else { return Promise.resolve(database); } }); }); return database_promise.then(function(database) { if (database) { const options = { isCaseSensitive: false, includeScore: true, shouldSort: true, // includeMatches: false, // findAllMatches: false, // minMatchCharLength: 1, // location: 0, threshold: 0.2, // distance: 100, // useExtendedSearch: false, ignoreLocation: true, // ignoreFieldNorm: false, // fieldNormWeight: 1, keys: [ "title" ] }; let curriculum_index={}; let topics_index={}; database.curriculum.forEach(c => curriculum_index[c.id]=c); database.topics.forEach(t => topics_index[t.id]=t); for (j=0; j

    Solutions
  • Textbooks
  • `); } function build_solutions() { if (Array.isArray(solution_search_result)) { const viewAllHTML = userSubscribed ? `View All` : ''; var solutions_section = $(`
  • Solutions ${viewAllHTML}
  • `); let questionUrl = "/questions/xxx/"; let askUrl = "/ask/question/xxx/"; solution_search_result.forEach((elem) => { let url = ('course' in elem)?askUrl:questionUrl; let solution_type = ('course' in elem)?'ask':'question'; let subtitle = ('course' in elem)?(elem.course??""):(elem.book ?? "")+"    "+(elem.chapter?"Chapter "+elem.chapter:""); solutions_section.find('#whiletyping-solutions').append(` ${elem.text} ${subtitle} `); }); $('#search-solution-options').empty(); if (Array.isArray(solution_search_result) && solution_search_result.length>0){ $('#search-solution-options').append(solutions_section); } MathJax.typesetPromise([document.getElementById('search-solution-options')]); } } function build_textbooks() { $('#search-pretype-options').empty(); $('#search-pretype-options').append($('#search-solution-options').html()); if (Array.isArray(textbook_search_result)) { var books_section = $(`
  • Textbooks View All
  • `); let searchUrl = "/books/xxx/"; textbook_search_result.forEach((elem) => { books_section.find('#whiletyping-books').append(` ${elem.title} ${ordinal(elem.edition)} ${elem.author} `); }); } if (Array.isArray(textbook_search_result) && textbook_search_result.length>0){ $('#search-pretype-options').append(books_section); } } function build_popup(first_time = false) { if ($('#search-text').val()=='') { build_pretype(); } else { solution_and_textbook_search(); } } var search_text_out = true; var search_popup_out = true; const is_login = false; const user_hash = null; function pretype_setup() { $('#search-text').focusin(function() { $('#search-popup').addClass('show'); resize_popup(); search_text_out = false; }); $( window ).resize(function() { resize_popup(); }); $('#search-text').focusout(() => { search_text_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-popup').mouseenter(() => { search_popup_out = false; }); $('#search-popup').mouseleave(() => { search_popup_out = true; if (search_text_out && search_popup_out) { $('#search-popup').removeClass('show'); } }); $('#search-text').on("keyup", delay(() => { build_popup(); }, 200)); build_popup(true); let prevbookUrl = `/search/pretype_books/`; let prebooks = null; try { prebooks = JSON.parse(localStorage.getItem('PRETYPE_BOOKS_'+(is_login?user_hash:'ANON'))); }catch(e) {} if (prebooks && 'previous_books' in prebooks && 'recommended_books' in prebooks) { if (is_login) { previous_books = prebooks.previous_books; recommended_books = prebooks.recommended_books; if (prebooks.time && new Date().getTime()-prebooks.time<1000*60*60*6) { build_popup(); return; } } else { anon_pretype(); return; } } $.ajax({ url: prevbookUrl, method: 'POST', data:{csrfmiddlewaretoken: "VZtGjycQuWtbnkaVgeN2J925moMjqBotS1zhJtOf3yhxncAVrekiux1grEQdoJqI"}, success: function(response){ previous_books = response.previous_books; recommended_books = response.recommended_books; if (is_login) { localStorage.setItem('PRETYPE_BOOKS_'+user_hash, JSON.stringify({ previous_books: previous_books, recommended_books: recommended_books, time: new Date().getTime() })); } build_popup(); }, error: function(response){ console.log(response); } }); } $( document ).ready(pretype_setup); $( document ).ready(function(){ $('#search-popup').on('click', '.search-view-item', function(e) { e.preventDefault(); let autoCompleteSearchViewUrl = `/search/autocomplete_search_view/`; let objectUrl = $(this).attr('href'); let selectedId = $(this).data('objid'); let searchResults = []; $("#whiletyping-solutions").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $("#whiletyping-books").find("a").each(function() { let is_selected = selectedId === $(this).data('objid'); searchResults.push({ objectId: $(this).data('objid'), contentType: $(this).data('contenttype'), category: $(this).data('category'), selected: is_selected }); }); $.ajax({ url: autoCompleteSearchViewUrl, method: 'POST', data:{ csrfmiddlewaretoken: "VZtGjycQuWtbnkaVgeN2J925moMjqBotS1zhJtOf3yhxncAVrekiux1grEQdoJqI", query: $('#search-text').val(), searchObjects: JSON.stringify(searchResults) }, dataType: 'json', complete: function(data){ window.location.href = objectUrl; } }); }); });
    Simultaneous Equations with Complex Coefficients Create a subroutine csimu1 to solve for the unknowns in a system of simultaneous linear equations that have complex coefficients. Test your subroutine by solving the system of equations shown below:  (-2+5  (2024)

    FAQs

    How do you solve simultaneous equations with coefficients? ›

    The most common method for solving simultaneous equations is the elimination method which means one of the unknowns will be removed from each equation. The remaining unknown can then be calculated. This can be done if the coefficient. In the example of 3a, the coefficient of a is 3 because 3 x a = 3a.

    How do you solve complex simultaneous equations? ›

    How to solve simultaneous equations
    1. Use the elimination method to get rid of one of the variables.
    2. Find the value of one variable.
    3. Find the value of the remaining variables using substitution.
    4. Clearly state the final answer.
    5. Check your answer by substituting both values into either of the original equations.

    What is 3x 2y 36 and 5x 4y 64? ›

    Example Solve the simultaneous equations 3x + 2y = 36 (1) 5x + 4y = 64 (2) . y = 6 Hence the full solution is x = 8, y = 6.

    How do you solve simultaneous equations y x 2 and y 3x 5? ›

    Expert-Verified Answer

    To solve the given simultaneous equations y = x - 2 and y = 3x + 5, the substitution method is used, leading to the solution x = -7/2 and y = -11/2.

    How do you solve a system of equations with coefficients? ›

    To Solve a System of Equations by Elimination
    1. Write both equations in standard form. ...
    2. Make the coefficients of one variable opposites. ...
    3. Add the equations resulting from Step 2 to eliminate one variable.
    4. Solve for the remaining variable.
    5. Substitute the solution from Step 4 into one of the original equations.

    What are the three methods of solving simultaneous equations? ›

    There are three methods by which simultaneous equations can be solved: elimination method, substitution method, graphing method. No matter which method is used, each method will lead to the same answer; however, there are times when one method leads to simpler calculations.

    What is a solved example of simultaneous equation? ›

    Simultaneous Equations Examples

    Answer: Solution of simultaneous equations 2x - y = 5 and y - 4x = 1 is x = -3 and y = -11. Example 2: Find the solution of the simultaneous equations 2x - 4y + z = 2, x + 5y - 3z = 7, 3x + 2y - z = 10 using the substitution method. Answer: Solution is x = 58/21, y = 19/21, and z = 2/21.

    What is the rule for solving simultaneous equations? ›

    If the signs are different, add the equations together. If the signs are the same, subtract them. You can remember this as DASS – Different Add, Same Subtract.

    How do you solve complex operations? ›

    To add two complex numbers , add the real part to the real part and the imaginary part to the imaginary part. To subtract two complex numbers, subtract the real part from the real part and the imaginary part from the imaginary part. To multiply two complex numbers, use the FOIL method and combine like terms .

    What is the solution to 4x 3y 4 6x 5y 8 simultaneous equation? ›

    The correct Answer is:(−2,4)

    How to solve 8x 5y 9 and 3x 2y 4 by substitution method? ›

    1. ∴y=9−8x5 ....(1)
    2. 3x+2y=4 ...(2) Substitute eq(1) in eq (2), we get.
    3. 3x+2(9−8x5)=4.
    4. 15x+18−16x=20. ⇒−x=2.
    5. ⇒x=−2. Substitute x=−2 in eq (1), we get.
    6. y=9−8(−2)5.
    7. ⇒y=255=5.
    8. So, (x,y)=(−2,5)

    What is the solution of 6x 4y =- 12 8x 3y =- 2? ›

    x=2,y=6.

    What is the solution of simultaneous equations 5x 3y 8 and 3x y 2? ›

    So, we have x=1andy=−1.

    How to solve 2x 3y 11 and 2x 4y =- 24 by cross multiplication method? ›

    In this question, we need to solve the two given equations: 2x + 3y = 11 and 2x − 4y = −24 and then use this solution set to find the value of m for which y = mx + 3. So, we have the solution set for the given pair of linear equations: x = -2 and y = 5.

    How many solutions does y 2x 5 and 8x 4y =- 20 have? ›

    –8x – 4y = –20. a. one solution: (–2.5, 0)

    How do you solve coefficient expressions? ›

    Step 1: Identify and separate all the terms of the algebraic expression. Make sure you keep the sign in front of the term with it. Step 2: Look for numerical values in front of the variables in each term to identify the coefficients. If there is no number in front, the coefficient is 1.

    How do you combine like terms with coefficients? ›

    When combining like terms, such as 2x and 3x, we add their coefficients. For example, 2x + 3x = (2+3)x = 5x.

    What do you do with coefficients when multiplying? ›

    The coefficients are multiplied separately as shown in the example.

    Do you multiply by coefficients? ›

    In math expressions, terms are the components added or subtracted, factors are the elements multiplied within each term, and coefficients are the numbers multiplying variables.

    References

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