{"id":302066,"date":"2022-09-10T22:12:39","date_gmt":"2022-09-10T16:42:39","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/if-the-system-of-equations-x2y3z%ce%bbx%e2%80%893xy2z%ce%bby%e2%80%892x3yz%ce%bbz-has-non-trivial-solution-then-%ce%bb\/"},"modified":"2022-09-10T22:12:39","modified_gmt":"2022-09-10T16:42:39","slug":"if-the-system-of-equations-x2y3z%ce%bbx%e2%80%893xy2z%ce%bby%e2%80%892x3yz%ce%bbz-has-non-trivial-solution-then-%ce%bb","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/if-the-system-of-equations-x2y3zx3xy2zy2x3yz\/","title":{"rendered":"If the system of equations \u00a0x+2y+3z=\u03bbx,\u20093x+y+2z=\u03bby,\u20092x+3y+z=\u03bbz\u00a0has non-trivial solution , then \u00a0\u03bb=\u2026\u2026.."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"If the system of equations \u00a0x+2y+3z=\u03bbx,\u20093x+y+2z=\u03bby,\u20092x+3y+z=\u03bbz\u00a0has non-trivial solution , then \u00a0\u03bb=\u2026\u2026..","custom_permalink":"question\/mathematics\/if-the-system-of-equations-x2y3zx3xy2zy2x3yz\/"},"categories":[],"acf":{"question":"<p>If the system of equations &nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><mi>y<\/mi><mo>+<\/mo><mn>3<\/mn><mi>z<\/mi><mo>=<\/mo><mi>\u03bb<\/mi><mi>x<\/mi><mo>,<\/mo><mtext>\u2009<\/mtext><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mi>y<\/mi><mo>+<\/mo><mn>2<\/mn><mi>z<\/mi><mo>=<\/mo><mi>\u03bb<\/mi><mi>y<\/mi><mo>,<\/mo><mtext>\u2009<\/mtext><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><mi>y<\/mi><mo>+<\/mo><mi>z<\/mi><mo>=<\/mo><mi>\u03bb<\/mi><mi>z<\/mi><\/math>&nbsp;has non-trivial solution , then &nbsp;<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>\u03bb<\/mi><\/math>=\u2026\u2026..<\/p>","options":[{"option":"<p>6<\/p>","correct":true},{"option":"<p>12<\/p>","correct":false},{"option":"<p>16<\/p>","correct":false},{"option":"<p>18<\/p>","correct":false}],"solution":"<p>Given system of equations ,&nbsp;<\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mfenced><mrow><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mrow><\/mfenced><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><mi>y<\/mi><mo>+<\/mo><mn>3<\/mn><mi>z<\/mi><mo>=<\/mo><mn>0<\/mn><mo>,<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mfenced><mrow><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mrow><\/mfenced><mo>+<\/mo><mn>2<\/mn><mi>z<\/mi><mo>=<\/mo><mn>0<\/mn><mo>,<\/mo><mtext>\u2009<\/mtext><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><mi>y<\/mi><mo>+<\/mo><mfenced><mrow><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mrow><\/mfenced><mi>z<\/mi><mo>=<\/mo><mn>0<\/mn><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtext>&nbsp;Has nontrivial solution&nbsp;<\/mtext><mo stretchy=\"false\">\u21d2<\/mo><mfenced separators=\"|\" close=\"|\" open=\"|\"><mtable columnalign=\"center center center\" columnspacing=\"1em\"><mtr><mtd><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><mtd><mn>2<\/mn><\/mtd><mtd><mn>3<\/mn><\/mtd><\/mtr><mtr><mtd><mn>3<\/mn><\/mtd><mtd><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><mtd><mn>2<\/mn><\/mtd><\/mtr><mtr><mtd><mn>2<\/mn><\/mtd><mtd><mn>3<\/mn><\/mtd><mtd><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><\/mtr><\/mtable><\/mfenced><mo>=<\/mo><mn>0<\/mn><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\"><mtr><mtd><msub><mi>R<\/mi><mn>1<\/mn><\/msub><mo>+<\/mo><msub><mi>R<\/mi><mn>2<\/mn><\/msub><mo>+<\/mo><msub><mi>R<\/mi><mn>3<\/mn><\/msub><\/mtd><\/mtr><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><mfenced separators=\"|\" close=\"|\" open=\"|\"><mtable columnalign=\"center center center\" columnspacing=\"1em\"><mtr><mtd><mn>6<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><mtd><mn>6<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><mtd><mn>6<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><\/mtr><mtr><mtd><mn>3<\/mn><\/mtd><mtd><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><mtd><mn>2<\/mn><\/mtd><\/mtr><mtr><mtd><mn>2<\/mn><\/mtd><mtd><mn>3<\/mn><\/mtd><mtd><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><\/mtr><\/mtable><\/mfenced><\/mtd><\/mtr><mtr><mtd><mo>(<\/mo><mn>6<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><mo>)<\/mo><mfenced separators=\"|\" close=\"|\" open=\"|\"><mtable columnalign=\"center center center\" columnspacing=\"1em\"><mtr><mtd><mn>1<\/mn><\/mtd><mtd><mn>1<\/mn><\/mtd><mtd><mn>1<\/mn><\/mtd><\/mtr><mtr><mtd><mn>3<\/mn><\/mtd><mtd><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><mtd><mn>2<\/mn><\/mtd><\/mtr><mtr><mtd><mn>2<\/mn><\/mtd><mtd><mn>3<\/mn><\/mtd><mtd><mn>1<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><\/mtd><\/mtr><\/mtable><\/mfenced><\/mtd><\/mtr><mtr><mtd><msub><mi>C<\/mi><mn>2<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>C<\/mi><mn>1<\/mn><\/msub><\/mtd><\/mtr><mtr><mtd><msub><mi>C<\/mi><mn>3<\/mn><\/msub><mo>\u2212<\/mo><msub><mi>C<\/mi><mn>1<\/mn><\/msub><\/mtd><\/mtr><\/mtable><\/math><\/p><p><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtable columnalign=\"right left right left right left right left right left right left\" columnspacing=\"0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em\"><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><mo>(<\/mo><mn>6<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><mo>)<\/mo><mfenced separators=\"|\" close=\"|\" open=\"|\"><mtable columnalign=\"center center\" columnspacing=\"1em\"><mtr><mtd><mn>1<\/mn><\/mtd><mtd><mn>0<\/mn><\/mtd><mtd><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd><mn>3<\/mn><\/mtd><mtd><mo>\u2212<\/mo><mi>\u03bb<\/mi><mo>\u2212<\/mo><mn>2<\/mn><\/mtd><mtd><mo>\u2212<\/mo><mn>1<\/mn><\/mtd><\/mtr><mtr><mtd><mn>2<\/mn><\/mtd><mtd><mn>1<\/mn><\/mtd><mtd><mo>\u2212<\/mo><mi>\u03bb<\/mi><mo>\u2212<\/mo><mn>1<\/mn><\/mtd><\/mtr><\/mtable><\/mfenced><mo>=<\/mo><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><mo>(<\/mo><mn>6<\/mn><mo>\u2212<\/mo><mi>\u03bb<\/mi><mo>)<\/mo><mo>[<\/mo><mo>(<\/mo><mi>\u03bb<\/mi><mo>+<\/mo><mn>1<\/mn><mo>)<\/mo><mo>(<\/mo><mi>\u03bb<\/mi><mo>+<\/mo><mn>2<\/mn><mo>)<\/mo><mo>+<\/mo><mn>1<\/mn><mo>]<\/mo><mo>=<\/mo><mn>0<\/mn><\/mtd><\/mtr><mtr><mtd><mo stretchy=\"false\">\u21d2<\/mo><mi>\u03bb<\/mi><mo>=<\/mo><mn>6<\/mn><mo>,<\/mo><msup><mi>\u03bb<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>3<\/mn><mi>\u03bb<\/mi><mo>+<\/mo><mn>3<\/mn><mo>=<\/mo><mn>0<\/mn><\/mtd><\/mtr><\/mtable><\/math><\/p>","subject":""},"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>If the system of equations \u00a0x+2y+3z=\u03bbx,\u20093x+y+2z=\u03bby,\u20092x+3y+z=\u03bbz\u00a0has non-trivial solution , then \u00a0\u03bb=\u2026\u2026.. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"If the system of equations \u00a0x+2y+3z=\u03bbx,\u20093x+y+2z=\u03bby,\u20092x+3y+z=\u03bbz\u00a0has non-trivial solution , then \u00a0\u03bb=\u2026\u2026..\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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