Using a matrix to solve the ax = b in this case is given as x₁ = (43)/3. See the explanation below.
A matrix is a set of integers that are organized in rows and columns to form a rectangular array.
[tex]\begin{bmatrix} 1& 1& 1\\ 1& 4& -1\\ 1& -1& 2\end{bmatrix}\begin{bmatrix} 1\\ 2\\3\end{bmatrix}[/tex]
R₁ → R₂ - R₁, R₃ → R₃ - R₁
[tex]\begin{bmatrix} 1& 1& 1\\ 0& 3& -2\\ 0& -2& 1\end{bmatrix}\begin{bmatrix} 1\\ 1\\2\end{bmatrix}[/tex]
R₃ → 3R₃+2R₂
[tex]\begin{bmatrix} 1& 1& 1\\ 0& 3& -2\\ 0& 0& 1\end{bmatrix}\begin{bmatrix} 1\\ 1\\8\end{bmatrix}[/tex]
⇒ -X₃ = 8
⇒ X₃ = -8
3x₂ + 16 = 0
⇒ x₂ = -16/3
Hence
X₁ + X₂ + X₃ = 1
Therefore
X₁ - (16/3) - 8 = 1
⇒ X1 - (40/3) = 1
⇒ X₁ = 1 + (40/3)
= 43/3
⇒ X₁ = 43/3
Learn more about matrixes:
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