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
x3435x121=x5x21(3)3x11\begin{vmatrix} x & -3 & 4 \\ 3 & -5 & x \\ 1 & 2 & -1 \\ \end{vmatrix}=x\begin{vmatrix} -5 & x \\ 2 & -1 \end{vmatrix}-(-3)\begin{vmatrix} 3 & x \\ 1 & -1 \end{vmatrix}

+43512=x(52x)+3(3x)+4(6+5)+4\begin{vmatrix} 3 & -5 \\ 1 & 2 \end{vmatrix}=x(5-2x)+3(-3-x)+4(6+5)

=5x2x293x+44=5x-2x^2-9-3x+44

=2x2+2x+35=45=-2x^2+2x+35=45

2x22x+10=02x^2-2x+10=0

x2x+5=0x^2-x+5=0

D=(1)24(1)(5)=19<0D=(-1)^2-4(1)(5)=-19<0

There is no solution for x.x.




23435x121=25x21(3)3x11\begin{vmatrix} 2 & -3 & 4 \\ 3 & -5 & x \\ 1 & 2 & -1 \\ \end{vmatrix}=2\begin{vmatrix} -5 & x \\ 2 & -1 \end{vmatrix}-(-3)\begin{vmatrix} 3 & x \\ 1 & -1 \end{vmatrix}

+43512=2(52x)+3(3x)+4(6+5)+4\begin{vmatrix} 3 & -5 \\ 1 & 2 \end{vmatrix}=2(5-2x)+3(-3-x)+4(6+5)

=104x93x+44=7x+45=45=10-4x-9-3x+44=-7x+45=45




x=0x=0

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