Question

Using matrices, solve the following system of linear equations: x+y+z=4
2x−y+z=−1
2x+y−3z=−9

Answer 1

Hello !!

For you answer this question, you only need make use of this method below. See the resolution.

Find (D).

$\left(\begin{array}{ccc}1&1&1\\2&-1&1\\2&1&-3\end{array}\right)\begin{array}{cc}1&1\\2&-1\\2&1\end{array}$

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D = 3 + 2 + 2 + 2 - 1 + 6

D = 5 + 2 + 2 - 1 + 6

D = 7 + 2 - 1 + 6

D = 9 - 1 + 6

D = 8 + 6

D = 14

Find Dz.

$\left(\begin{array}{ccc}1&1&4\\2&-1&-1\\2&1&-9\end{array}\right)\begin{array}{cc}1&1\\2&-1\\2&1\end{array}$

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Dz = 9 - 2 + 8 + 8 + 1 + 18

Dz = 7 + 8 + 8 + 1 + 18

Dz = 15 + 8 + 1 + 18

Dz = 23 + 1 + 18

Dz = 24 + 18

Dz = 42

Find Dy.

$\left(\begin{array}{ccc}1&4&1\\2&-1&1\\2&-9&-3\end{array}\right)\begin{array}{cc}1&4\\2&-1\\2&-9\end{array}$

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Dy = 3 + 8 - 18 + 2 + 9 + 24

Dy = 11 - 18 + 2 + 9 + 24

Dy = -7 + 2 + 9 + 24

Dy = -5 + 9 + 24

Dy = 4 + 24

Dy = 28

Find Dx.

$\left(\begin{array}{ccc}4&1&1\\-1&-1&1\\-9&1&-3\end{array}\right)\begin{array}{cc}4&1\\-1&-1\\-9&1\end{array}$

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Dx = 12 - 9 - 1 - 9 - 4 - 3

Dx = 3 - 1 - 9 - 4 - 3

Dx = 2 - 9 - 4 - 3

Dx = -7 - 4 - 3

Dx = -11 - 3

Dx = -14

Find the solution for (x).

x = Dx/D = -14/14 = -1

Find the solution for (y).

y = Dy/D = 28/14 = 2

Find the solution for (z).

z = Dz/D = 42/14 = 3

Final result : The solution for (x) is -1, the solution for (y) is 2 and the solution for (z) is 3.

I hope I have collaborated !