Answer to Question #236240 in Linear Algebra for luka

Question #236240

Using matrix method, solve the simultaneous equations {x-3y=3

5x-9y=11


1
Expert's answer
2021-09-20T17:34:28-0400

"A\\bar x=\\bar b"

"A=\\begin{pmatrix}\n 1 & -3 \\\\\n 5 & -9\n\\end{pmatrix},\\bar b=\\begin{pmatrix}\n 3 \\\\\n 11\n\\end{pmatrix}" .

"det(A)=-9+15=6."

"A^{-1}=\\frac{1}{6}\\begin{pmatrix}\n -9 & 3 \\\\\n -5 & 1\n\\end{pmatrix}"

"\\bar x=\\begin{pmatrix}\n x \\\\\n y\n\\end{pmatrix}=A^{-1}\\bar b=\\frac{1}{6}\\begin{pmatrix}\n -9& 3 \\\\\n -5 & 1\n\\end{pmatrix}\\begin{pmatrix}\n 3 \\\\\n 11\n\\end{pmatrix}=\\frac{1}{6}\\begin{pmatrix}\n 6 \\\\\n -4\n\\end{pmatrix}=\\begin{pmatrix}\n 1 \\\\\n -\\frac{2}{3}\n\\end{pmatrix}"

Thus, "x=1,y=-\\frac{2}{3}."



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