How to solve the following systems of simultaneous equations using matrices? 1) 2x+3y-z=12 2y+z=7 2y-z=5

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How to solve the following systems of simultaneous equations using matrices? 1) 2x+3y-z=12 2y+z=7 2y-z=5

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Answer 1 · 2018-01-30T11:27:37

$x = 2, y = 3 and z = 1$ $x=2,y=3 and z=1$
Shown 1 step at a time. By the time you have checked through 'this lot' the method will be truly fixed in your mind!

Explanation:

By example: using the convention type: $R_{2}$ $R_2$ representing row 2

$The objective is to have the condition listed below$ $color(brown)("The objective is to have the condition listed below")$
$All manipulation is to achieve this goal .$ $color(brown)("All manipulation is to achieve this goal".)$

The value of 1 under $x$ $x$ in $R_{1}$ $R_1$ and zeros under $y and z$ $y and z$
means that you only have $x$ $x$ in that row.

The value of 1 under $y$ $y$ in $R_{2}$ $R_2$ and zeros under $x and z$ $x and z$ means that you only have $y$ $y$ in that row.

The value of 1 under $z$ $z$ in $R_{3}$ $R_3$ and zeros under $x and y$ $x and y$ means that you only have $z$ $z$ in that row.

$\approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx \approx$ $color(brown)(~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~)$

$color(green)(((x,y,z,|,"answer"),(2,3,-1,|,12),(0,2,1,|,7),(0,2,-1,|,5) ))$
$color(white)("dddd")R_2xx1/2$ Turns the 2 in $R_2$ into 1
$color(white)("dddddd")darr$

$color(green)(((2,3,-1,|,12),(0,1,1/2,|,7/2),(0,2,-1,|,5) ))$
$color(white)("ddd"2/2)R_3-2R_2$
$color(white)("ddddddd")darr$

$color(green)(((2,3,-1,|,12),(0,1,1/2,|,7/2),(0,0,-2,|,-2) ))$
$color(white)("ddd"2/2)R_3xx(-1/2)$
$color(white)("dddddddd")darr$

$color(green)(((2,3,-1,|,12),(0,1,1/2,|,7/2),(0,0,1,|,1) ))$
$color(white)("ddd"2/2)R_2-1/2R_3$
$color(white)("dddddddd")darr$

$color(green)(((2,3,-1,|,12),(0,1,0,|,3),(0,0,1,|,1) ))$
$color(white)("ddd"2/2)R_1xx1/2$
$color(white)("dddddddd")darr$

$color(green)(((1,3/2,-1/2,|,6),(0,1,0,|,3),(0,0,1,|,1) ))$
$color(white)("ddd"2/2)R_1-3/2R_2$
$color(white)("dddddddd")darr$

$color(green)(((1,0,-1/2,|,3/2),(0,1,0,|,3),(0,0,1,|,1) ))$
$color(white)("ddd"2/2)R_1+1/2R_3$
$color(white)("dddddddd")darr$

$color(green)(((1,0,0,|,2),(0,1,0,|,3),(0,0,1,|,1) ))$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Check

$x=2,y=3 and z=1$

$2x+3y-z=12 -> 2(2)+3(3)-(1) ->12 color(red)(larr" True")$

$2y+z=7 -> 2(3)+1 ->7 color(red)(larr" True")$

$2y-z=5->2(3)-1->5 color(red)(larr" True")$

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How to solve the following systems of simultaneous equations using matrices? 1) 2x+3y-z=12 2y+z=7 2y-z=5

1 Answer

Explanation:

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