Answer to Question #349894 in Linear Algebra for Busi

Question #349894

Solve for x in the given matrix equalities



det (x −3 4


3 −5 x


1 2 −1)= 45


1
Expert's answer
2022-06-13T18:06:17-0400
"\\begin{vmatrix}\n x & -3 & 4 \\\\\n 3 & -5 & x \\\\\n 1 & 2 & -1 \\\\\n\\end{vmatrix}=x\\begin{vmatrix}\n -5 & x \\\\\n 2 & -1\n\\end{vmatrix}-(-3)\\begin{vmatrix}\n 3 & x \\\\\n 1 & -1\n\\end{vmatrix}"

"+4\\begin{vmatrix}\n 3 & -5 \\\\\n 1 & 2\n\\end{vmatrix}=x(5-2x)+3(-3-x)+4(6+5)"

"=5x-2x^2-9-3x+44"

"=-2x^2+2x+35=45"

"2x^2-2x+10=0"

"x^2-x+5=0"

"D=(-1)^2-4(1)(5)=-19<0"

There is no solution for "x."




"\\begin{vmatrix}\n 2 & -3 & 4 \\\\\n 3 & -5 & x \\\\\n 1 & 2 & -1 \\\\\n\\end{vmatrix}=2\\begin{vmatrix}\n\n -5 & x \\\\\n\n 2 & -1\n\n\\end{vmatrix}-(-3)\\begin{vmatrix}\n\n 3 & x \\\\\n\n 1 & -1\n\n\\end{vmatrix}"

"+4\\begin{vmatrix}\n 3 & -5 \\\\\n 1 & 2\n\\end{vmatrix}=2(5-2x)+3(-3-x)+4(6+5)"

"=10-4x-9-3x+44=-7x+45=45"




"x=0"

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