Question

Find the system of linear equations represented by the augmented matrix. Then use back substitution to solve. (Use variables x, y, z, and w if applicable.)

[ 1 2 -2 : 3
0 1 1 : -15
0 0 1 : -5 ]
(x, y, z) = ______.

Answer 1

x = 13 y = - 10 z = -5

Explanation:

In the augmented matrix of a system of linear equation, each row represent an equation, and each column represent variables and constants

Therefore the linear equation for the augmented matrix

1 2 -2 : 3

0 1 1 : -15

0 0 1 : -5

Is in terms of x y z and w, the equation system:

1*x + 2*y - 2*z = 3

0*x + 1* y + 1*z = -15

0*x + 0*y + 1*z = -5

To solve it we proceed as follows

from the last equation z = - 5

plugging this value in the second equation

y + z = - 15

y - 5 = - 15

y = - 10

And finally

x + (2)*(-10) - 2*( - 5 ) = 3

x - 20 + 10 = 3

x - 10 = 3

x = 13