2 x &#x2212;<!-- − --> 3 y + 4 z = &#x2212;<!-- − --> 19 <mspac

osmane5e

osmane5e

Answered question

2022-05-26

2 x 3 y + 4 z = 19 6 x + 4 y 2 z = 8 x + 5 y + 4 z = 23
what I have done so far is I put the nubmer and x,y and z in matrix form:
[ 2 3 4 6 4 2 1 5 4 ] [ x y z ] = [ 19 8 23 ]

Answer & Explanation

Hugo Bruce

Hugo Bruce

Beginner2022-05-27Added 10 answers

You can use Gaussian Elimination on the augmented coefficient matrix to solve for x , y , z by expressing the matrix in reduced row echelon form.
[ 2 3 4 19 6 4 2 8 1 5 4 23 ]
If you do this correctly, you should obtain the following:
[ 1 0 0 20 / 9 0 1 0 7 / 9 0 0 1 38 / 9 ]
This means that
[ x y z ] = [ 20 / 9 7 / 9 38 / 9 ]
Ashly Harrell

Ashly Harrell

Beginner2022-05-28Added 4 answers

You can also use Cramer's Rule:
x = | 19 3 4 8 4 2 23 5 4 | | 2 3 4 6 4 2 1 5 4 | = 2
y = | 2 19 4 6 8 2 1 23 4 | | 2 3 4 6 4 2 1 5 4 | = 5
z = | 2 3 19 6 4 8 1 5 23 | | 2 3 4 6 4 2 1 5 4 | = 0
In the numerator, replace the column in the matrix corresponding to the given variable by the column of results. Note that the bars denote the determinant of the matrix.

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