Answer to Question #136020 in Analytic Geometry for Yolanda

Question #136020
use matrices and elementary row operations to solve 5x-3y+2z=13, 2x-y-3z=1,4x-2y+4z=12
1
Expert's answer
2020-10-01T13:01:10-0400

"\\begin{aligned}\\left(\\begin{array}{rrr|r}\n5 & -3 & 2 & 13\\\\\n2& -1 & -3 & 1 \\\\\n 4 & -2 & 4 & 12\\\\\n\\end{array}\\right) &{\\stackrel{2R_2}{\\rightarrow}} \\left(\\begin{array}{rrr|r}\n5 & -3 & 2 & 13\\\\\n4& -2 & -6 & 2 \\\\\n 4 & -2 & 4 & 12\\\\\n\\end{array}\\right) \\\\&{\\stackrel{R_3 - R_2}{\\rightarrow}} \\left(\\begin{array}{rrr|r}\n5 & -3 & 2 & 13\\\\\n4& -2 & -6 & 2 \\\\\n 0 & 0 & 10 & 10\n\\end{array}\\right) \\\\&{\\stackrel{R_1 \\times 4, R_2 \\times 5}{\\rightarrow}}\\left(\\begin{array}{rrr|r}\n20 & -12 & 8 & 52\\\\\n20& -10 & -30& 10 \\\\\n 0 & 0 & 10 & 10\n\\end{array}\\right)\\\\&{\\stackrel{R_2 - R_1}{\\rightarrow}}\\left(\\begin{array}{rrr|r}\n20 & -12 & 8& 52\\\\\n0& 2 & -38& -42 \\\\\n 0 & 0 & 10 & 10\n\\end{array}\\right)\n\\end{aligned}\\\\\n\\textsf{By back substitution,}\\\\\n10z = 10, \\Rightarrow z = 1\\\\ \n2y - 38z = -42, 2y - 38(1) = -42, \\\\ 2y = 38 - 42, 2y = -4, y = -2\\\\\n20x - 12y + 8z = 52 \\\\\n20x - 12(-2) + 8(1) = 52 \\\\\n20x + 24 + 8 = 52 \\\\\n20x + 32 = 52\\\\\n20x = 20 \\Rightarrow x = 1\\\\\n\\therefore x = 1, y = - 2 \\hspace{0.1cm}\\textsf{and}\\hspace{0.1cm} z = 1 \\\\\\textsf{are the solutions to}\\\\\\textsf{the simultaneous equations}"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS