Question 315233
[A]={{{(matrix(2,2,3,-4,5,2))}}}
[b]={{{(matrix(2,1,12,-6))}}}
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Find the determinant of [A].
det[A]={{{3(2)-(5)(-4)=26}}}
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Replace the first column of [A] with [b]
[Ax]={{{(matrix(2,2,12,-4,-6,2))}}}
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Calculate this determinant.
det[Ax]={{{12(2)-(-6)(-4)=0}}}
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Calculate {{{x}}}.
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x=det[Ax]/det[A]
{{{x=0/26}}}
{{{highlight( x=0)}}}
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Replace the second column of [A] with [b]
[Ay]={{{(matrix(2,2,3,12,5,-6))}}}
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Calculate this determinant.
det[Ax]={{{(3)(-6)-5(12)=-78}}}
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Calculate {{{y}}}.
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y=det[Ay]/det[A]
{{{y=-78/26}}}
{{{highlight(y=-3)}}}