InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
x-y+z=4x+y+z=22x+y-3z=0 |
| Answer» {tex}A = \\left[ {\\begin{array}{*{20}{c}} 1&{ - 1}&1 \\\\ 2&1&{ - 3} \\\\ 1&1&1 \\end{array}} \\right]{/tex}{tex}\\left| A \\right| = \\left[ {\\begin{array}{*{20}{c}} 1&{ - 1}&1 \\\\ 2&1&{ - 3} \\\\ 1&1&1 \\end{array}} \\right]{/tex}{tex} = 10 \\ne 0{/tex}Here,A11 = 4, A12 = -5, A13 = 1A21 = 2, A22 = 0, A23 = -2A31 = 2, A32 = 5, A33 = 3{tex}adjA = \\left[ {\\begin{array}{*{20}{c}} 4&2&2 \\\\ { - 5}&0&5 \\\\ 1&{ - 2}&3 \\end{array}} \\right]{/tex}{tex}{A^{ - 1}} = \\frac{1}{{\\left| A \\right|}}\\left( {adjA} \\right){/tex}{tex}= \\frac{1}{{10}}\\left[ {\\begin{array}{*{20}{c}} 4&2&2 \\\\ { - 5}&0&5 \\\\ 1&{ - 2}&3 \\end{array}} \\right]{/tex}System of equation can be written isX = A-1B{tex} = \\frac{1}{{10}}\\left[ {\\begin{array}{*{20}{c}} 4&2&2 \\\\ { - 5}&0&5 \\\\ 1&{ - 2}&3 \\end{array}} \\right]\\left[ {\\begin{array}{*{20}{c}} 4 \\\\ 0 \\\\ 2 \\end{array}} \\right]{/tex}{tex}\\left[ {\\begin{array}{*{20}{c}} x \\\\ y \\\\ z \\end{array}} \\right] = \\left[ {\\begin{array}{*{20}{c}} 2 \\\\ { - 1} \\\\ 1 \\end{array}} \\right]{/tex}x = 2, y = -1, z = 1 | |