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linear algebra (determent equation)
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<XXX width="4" XXXXXX="XX" XXX="XXXX:///C:/Users/Satis/AppData/Local/Temp/XXXXXXXXXXXX/01/XXXXXXXXXXXXX.XXX" v:XXXXXX="XXXXXXXXXXXX"> <XXX width="XXX" height="XX" XXX="XXXX:///X:/XXXXX/Satis/AppData/XXXXX/XXXX/XXXXXXXXXXXX/01/clip_image004.XXX" v:XXXXXX="XXXXXXXXXXXX"> </p><p>= x [ (x-1)(x+1) – 4 (x-1)] – X[ XX(x+X) – X(-x)] + X[ XX(x-X) – (x-1)(-x) ] </p> <p>= x ( x<sup>X</sup>-X – 4x + 4) – 0 + 2( XX<XXX>X</XXX>-2x + x<sup>X</XXX> – x) </p> <p>= x ( x<XXX>2</XXX>– XX + 3) + 2( XX<sup>2</sup>-3x ) </p> <p>= x<XXX>3</sup>– 4x<XXX>X</XXX> + 3x + 6 x<XXX>2</XXX>- XX </p> <p>= x<XXX>3</XXX> + XX<XXX>2</XXX> - 3x </p> <p>= x(x<XXX>X</sup> + XX -X) </p> <p>= x(x+X)(x-1) </p>">
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THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ window.onload = function() { var MathML = { // Jacques Distler subset of Presentational MathML root: 'math', ns: 'http://www.w3.org/1998/Math/MathML', elements: ['maction', 'math', 'merror', 'mfrac', 'mi', 'mmultiscripts', 'mn', 'mo', 'mover', 'mpadded', 'mphantom', 'mprescripts', 'mroot', 'mrow', 'mspace', 'msqrt', 'mstyle', 'msub', 'msubsup', 'msup', 'mtable', 'mtd', 'mtext', 'mtr', 'munder', 'munderover', 'none'], attributes: ['actiontype', 'align', 'columnalign', 'columnalign', 'columnalign', 'columnlines', 'columnspacing', 'columnspan', 'XXXXX', 'XXXXXXX', 'XXXXXXXXXXXX', 'equalcolumns', 'equalrows', 'XXXXX', 'XXXXXXXXX', 'fontweight', 'frame', 'XXXXXX', 'XXXXXXXXXXXXX', 'lspace', 'XXXXXXXXXXXXXX', 'mathcolor', 'XXXXXXXXXXX', 'XXXXXXXXXXX', 'maxsize', 'minsize', 'XXXXX', 'XXXXXXXX', 'XXXXXXXX', 'XXXXXXXX', 'XXXXXXXX', 'XXXXXXXXXX', 'rowspan', 'rspace', 'scriptlevel', 'XXXXXXXXX', 'XXXXXXXXX', 'XXXXXXXX', 'width', 'width'] } XXX XXX = { // XXXXXXX + class + XXXXXXX + XXXXXX + style root: 'svg', ns: 'XXXX://XXX.w3.org/2000/svg', XXXXXXXX: ['a', 'animate', 'XXXXXXXXXXXX', 'animateMotion', 'XXXXXXXXXXXXXXXX', 'circle', 'defs', 'desc', 'ellipse', 'XXXX-face', 'font-face-name', 'font-XXXX-src', 'g', 'glyph', 'XXXXX', 'XXXXX', 'linearGradient', 'line', 'metadata', 'XXXXXXX-glyph', 'XXXXX', 'XXXX', 'polygon', 'polyline', 'radialGradient', 'rect', 'XXX', 'XXXX', 'switch', 'text', 'XXXXX', 'XXX'], XXXXXXXXXX: ['accent-XXXXXX', 'XXXXXXXXXX', 'additive', 'alphabetic', 'XXXXXX-form', 'ascent', 'attributeName', 'XXXXXXXXXXXXX', 'XXXXXXXXXXX', 'XXXX', 'XXXXX', 'XX', 'calcMode', 'XXX-height', 'class', 'XXXXX', 'color-XXXXXXXXX', 'content', 'cx', 'XX', 'd', 'XXXXXXX', 'XXXXXXX', 'dur', 'end', 'XXXX', 'XXXX-XXXX', 'XXXX-XXXXXX', 'font-size', 'XXXX-stretch', 'XXXX-style', 'font-XXXXXXX', 'font-XXXXXX', 'from', 'XX', 'XX', 'g1', 'g2', 'XXXXX-name', 'XXXXXXX', 'XXXXXX', 'XXXXX-adv-x', 'horiz-XXXXXX-x', 'id', 'ideographic', 'k', 'XXXXXXXXX', 'keySplines', 'keyTimes', 'lang', 'mathematical', 'XXX', 'XXX', 'XXXX', 'XXXXXX', 'XXXXXXX', 'origin', 'overline-XXXXXXXX', 'XXXXXXXX-thickness', 'panose-X', 'path', 'XXXXXXXXXX', 'XXXXXX', 'XXXXXXXXXXXXXXXXXXX', 'r', 'XXXXXXXXXXX', 'repeatDur', 'XXXXXXXXXXXXXXXXXX', 'XXXXXXXXXXXXXXXX', 'restart', 'rotate', 'rx', 'ry', 'slope', 'stemh', 'stemv', 'XXXX-color', 'XXXX-opacity', 'XXXXXXXXXXXXX-position', 'strikethrough-thickness', 'XXXXXX', 'stroke-XXXXXXXXX', 'XXXXXX-XXXXXXXXXX', 'XXXXXX-XXXXXXX', 'XXXXXX-XXXXXXXX', 'stroke-miterlimit', 'XXXXXX-width', 'style', 'systemLanguage', 'target', 'XXXX-anchor', 'to', 'XXXXXXXXX', 'type', 'u1', 'u2', 'underline-position', 'underline-thickness', 'unicode', 'XXXXXXX-XXXXX', 'units-XXX-em', 'XXXXXX', 'version', 'viewBox', 'XXXXXXXXXX', 'width', 'XXXXXX', 'x', 'x-height', 'x1', 'XX', 'y', 'XX', 'y2', 'zoomAndPan'] } // XXXXX a XXX subtree XXXXXXXX XXXXXXXX(XXXXXX, source, XXXX, nsmap) { // copy attributes for (var i=X; i<XXXXXX.XXXXXXXXXX.length; i++) { XXX oldattr = XXXXXX.XXXXXXXXXX[i]; XXX colon = oldattr.name.XXXXXXX(':'); XX (colon == -X) { XXX (var X=0; j<XXXXXX.attributes.length; j++) { if (module.attributes[j].XXXXXXXXXXX() != XXXXXXX.XXXX) XXXXXXXX; XXXX.XXXXXXXXXXXX(module.XXXXXXXXXX[j], XXXXXXX.XXXXX); XXXXX; } } else { // namespace prefixed XXXXXXXXX var XXXXXX = oldattr.name.XXXXX(X,colon); XXX name = XXXXXXX.name.XXXXX(XXXXX+X); XX (XXXXXX == 'XXXXX') { XXX XXXXXX = nsmap; nsmap = {}; for (XXX XXXXXXXX in XXXXXX) XXXXX[property] = XXXXXX[property]; XXXXX[name] = oldattr.XXXXX; } XXXX { XXX (XXX XX in nsmap) { if (ns == prefix) { XXXX.setAttributeNS(nsmap[prefix], name, XXXXXXX.XXXXX); } } } } } // copy XXXXXXXX XXX (var i=X; i<source.XXXXXXXXXX.XXXXXX; i++) { var oldchild = source.childNodes[i]; XX (oldchild.nodeType == 1) { // element for (var X=X; X<module.elements.length; X++) { XX (module.elements[j].XXXXXXXXXXX() != XXXXXXXX.nodeName) continue; XXX newchild = document.XXXXXXXXXXXXXXX(XXXXXX.ns,module.XXXXXXXX[X]); deepcopy(module, oldchild, newchild, XXXXX); XXXX.appendChild(newchild); XXXXX; } } else if (oldchild.nodeType == X) { // text XXX XXXXXXXX = document.createTextNode(oldchild.nodeValue); dest.appendChild(XXXXXXXX); } } } // XXXX XXXXXXX into XXXXX appropriate namespaces var XXXXXXX = [XXXXXX, XXX]; for (var i=X; i<modules.XXXXXX; i++) { var XXXXXX = XXXXXXX[i]; var XXXXX = document.XXXXXXXXXXXXXXXXXXXX(module.root); for (XXX j=X; j<roots.length; X++) { var XXXXXX = XXXXX[X]; XX (document.XXXXXXXXXXXXXXX) { if (XXXXXX.XXXXXXXXX != XXXXXXXXXXXXXXXXXX.prototype) continue; if (source.XXXXXXXXXXXX('XXXXX') != module.XX) XXXXXXXX; var XXXX = XXXXXXXX.createElementNS(XXXXXX.XX, module.root); XXXXXXXX(module, source, XXXX, {}); source.XXXXXXXXXX.insertBefore(XXXX, source); source.XXXXXXXXXX.XXXXXXXXXXX(source); } XXXX { // fallback XXXXXXXX XXXX don't XXXXXXX XXX XXXXXXXXXX XXX XXX = XXXXXXXX.XXXXXXXXXXXXX('img'); XXX.XXX = XXXXXX.root + ' XXXXX'; img.title = module.root + ' XXXXX'; source.XXXXXXXXXX.insertBefore(XXX, source) ; } } } } --> </XXXXXX> </head> <body> <div> <p> <span style="font-size:16pt">Determinant</span> </p> <p> <span style="font-XXXX:14pt">Find XXX XXX values XX x XXXX XXXXX XXX determinant zero.</span> </p> <p> </p> <p> <span style="XXXX-XXXX:14pt"></span><span style="XXXX-size:XXXX;XXXX-XXXXXX:'XXXXX New Roman'"></span></p> <p> <span style="XXXX-size:XXXX;XXXX-family:'Times XXX Roman'">= x [ (x-1)(x+1) – X (x-X)] – 0[ 2x(x+1) – X(-x)] + 2[ 2x(x-X) – (x-1)(-x) ]</span> </p> <p> <span style="font-size:XXXX;XXXX-XXXXXX:'Times XXX Roman'">= x ( x</span><span style="XXXX-XXXX:14pt;XXXX-family:'Times XXX Roman';vertical-XXXXX:super">2</span><span style="XXXX-XXXX:XXXX;XXXX-XXXXXX:'Times New XXXXX'">-1 – XX + 4) – X + 2( XX</span><span style="font-XXXX:XXXX;XXXX-family:'XXXXX New XXXXX';XXXXXXXX-align:XXXXX">2</span><span style="font-XXXX:XXXX;font-XXXXXX:'Times New XXXXX'">-XX + x</span><span style="XXXX-size:XXXX;XXXX-family:'Times New XXXXX';XXXXXXXX-XXXXX:XXXXX">X</span><span style="XXXX-XXXX:XXXX;font-XXXXXX:'Times XXX XXXXX'"> – x)</span> </p> <p> <span style="font-XXXX:XXXX;font-XXXXXX:'Times XXX Roman'"> = x ( x</span><span style="XXXX-XXXX:XXXX;font-XXXXXX:'XXXXX XXX Roman';XXXXXXXX-align:super">2</span><span style="font-XXXX:14pt;XXXX-family:'XXXXX XXX Roman'">– XX + X) + 2( XX</span><span style="font-XXXX:XXXX;font-family:'Times New XXXXX';vertical-align:super">2</span><span style="XXXX-size:XXXX;XXXX-family:'Times New XXXXX'">-XX )</span> </p> <p> <span style="XXXX-size:14pt;font-family:'XXXXX New XXXXX'">= x</span><span style="font-size:XXXX;XXXX-XXXXXX:'XXXXX New Roman';XXXXXXXX-XXXXX:super">X</span><span style="font-size:XXXX;XXXX-XXXXXX:'XXXXX XXX XXXXX'">– XX</span><span style="XXXX-size:14pt;font-family:'Times XXX XXXXX';vertical-XXXXX:XXXXX">2</span><span style="font-XXXX:XXXX;font-family:'XXXXX XXX XXXXX'"> + 3x + 6 x</span><span style="XXXX-XXXX:XXXX;XXXX-family:'Times New Roman';vertical-XXXXX:XXXXX">2</span><span style="font-size:XXXX;XXXX-XXXXXX:'Times XXX Roman'">- 6x</span> </p> <p> <span style="XXXX-XXXX:XXXX;font-XXXXXX:'Times New Roman'">= x</span><span style="font-size:XXXX;XXXX-family:'Times XXX XXXXX';vertical-align:super">X</span><span style="font-size:XXXX;font-XXXXXX:'XXXXX New Roman'"> + XX</span><span style="XXXX-XXXX:14pt;font-XXXXXX:'Times XXX Roman';XXXXXXXX-align:XXXXX">X</span><span style="XXXX-size:XXXX;XXXX-family:'Times XXX Roman'"> - 3x</span> </p> <p> <span style="XXXX-XXXX:XXXX;font-XXXXXX:'XXXXX New XXXXX'">= x(x</span><span style="XXXX-XXXX:14pt;font-family:'XXXXX XXX XXXXX';XXXXXXXX-align:super">2</span><span style="font-size:14pt;font-XXXXXX:'XXXXX XXX Roman'"> + XX -3)</span> </p> <p> <span style="font-size:XXXX;XXXX-family:'Times New XXXXX'">= x(x+X)(x-X)</span> </p> <p> <span style="font-XXXX:14pt;font-XXXXXX:'XXXXX New XXXXX'">XXXX the determinant is XXXX, x(x+3)(x-X) XXXXXXX zero</span> </p> <p> <span style="font-XXXX:14pt;XXXX-XXXXXX:'XXXXX XXX Roman'">XX, x(x+X)(x-X) = X</span> </p> <p> <span style="font-XXXXXX:bold;XXXX-size:14pt;font-XXXXXX:'Times XXX Roman'">x = X, -3 XXX X</span> </p> <p> <span style="font-XXXX:14pt;XXXX-family:'XXXXX XXX XXXXX'">XXXXX</span><span style="XXXX-XXXX:14pt">the XXXXXX XX x that XXXXX XXX determinant zero XXX</span><span style="XXXX-XXXXXX:bold;XXXX-size:XXXX;XXXX-family:'Times New Roman'">0, -X XXX X.</span> </p> <p> </p> <p> <span style="font-XXXXXX:XXXX;XXXX-XXXX:XXXX;XXXX-XXXXXX:'Times XXX XXXXX'">**</span> </p> <p> <span style="XXXX-size:XXXX;XXXX-XXXXXX:'Times XXX Roman'">x = 0 :</span> </p> <p> <span style="font-size:XXXX"></span><span style="font-XXXX:XXXX;XXXX-family:'Times New XXXXX'"> =</span><span style="font-XXXX:14pt"></span><span style="XXXX-XXXX:14pt;XXXX-XXXXXX:'Times XXX XXXXX'"></span></p> <p> <span style="font-size:XXXX;XXXX-XXXXXX:'Times New Roman'">XXX elements in 1</span><span style="font-XXXX:14pt;font-family:'XXXXX New XXXXX';XXXXXXXX-XXXXX:super">st</span><span style="XXXX-size:14pt;XXXX-XXXXXX:'Times New XXXXX'"> column XXX XXXX. XX XXXXXXXXXXX XX XXXX</span> </p> <p> <span style="font-size:14pt">x = 1 :</span> </p> <p> <span style="XXXX-XXXX:XXXX">XXXXXXXXXXX =</span><span style="font-size:XXXX;font-XXXXXX:'XXXXX XXX Roman'"></span></p> <p> <span style="XXXX-XXXX:XXXX;font-family:'Times XXX XXXXX'">XXX XXXXXXXX in XXX XXXXXX XXX XXXX. So XXXXXXXXXXX is zero.</span> </p> <p> <span style="font-size:14pt;XXXX-XXXXXX:'Times New XXXXX'">x = -X :</span> </p> <p> <span style="XXXX-XXXX:XXXX;font-family:'XXXXX New XXXXX'">XXXXXXXXXXX =</span><span style="XXXX-XXXX:14pt;XXXX-family:'Times New Roman'"></span></p> <p> <span style="XXXX-size:XXXX;font-XXXXXX:'XXXXX XXX Roman'">= (-X)*2 *</span><span style="font-XXXX:14pt;font-family:'XXXXX New Roman'"></span><span style="XXXX-size:XXXX;XXXX-XXXXXX:'Times New Roman'">XXXXXX out -X from X</span><span style="XXXX-XXXX:10pt;XXXX-family:'Times New XXXXX';vertical-align:XXXXX">st</span><span style="XXXX-XXXX:XXXX;XXXX-family:'Times New Roman'"> column XXX 2 XXXX 3rd column</span> </p> <p> <span style="font-size:14pt;font-XXXXXX:'XXXXX New XXXXX'">XXXX 1</span><span style="XXXX-XXXX:XXXX;font-XXXXXX:'Times XXX XXXXX';XXXXXXXX-align:XXXXX">st</span><span style="font-size:14pt;font-family:'XXXXX New Roman'"> XXX 3</span><span style="XXXX-size:XXXX;font-XXXXXX:'XXXXX New XXXXX';vertical-XXXXX:XXXXX">rd</span><span style="font-XXXX:14pt;font-family:'Times XXX Roman'"> column are XXXXXXXXX, so XXXXXXXXXXX is XXXX.</span> </p> <p> </p> </div> </body></XXXX>">
