Using matrices, solve the system of linear equations: $x + y = 3$ and $2x - y = 3$.

Question

Accepted Answer

Represent the system in matrix form $AX = B$:
$$\begin{pmatrix} 1 & 1 \ 2 & -1 \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 3 \ 3 \end{pmatrix}$$

**Step 1: Find determinant of matrix $A$**
$$|A| = (1)(-1) - (1)(2) = -1 - 2 = -3 
eq 0$$

**Step 2: Find $A^{-1}$**
$$A^{-1} = \frac{1}{-3} \begin{pmatrix} -1 & -1 \ -2 & 1 \end{pmatrix} = \begin{pmatrix} 1/3 & 1/3 \ 2/3 & -1/3 \end{pmatrix}$|

**Step 3: Compute $X = A^{-1}B$**
$$\begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} 1/3 & 1/3 \ 2/3 & -1/3 \end{pmatrix} \begin{pmatrix} 3 \ 3 \end{pmatrix}$$
$$\begin{pmatrix} x \ y \end{pmatrix} = \begin{pmatrix} (1/3)(3) + (1/3)(3) \ (2/3)(3) + (-1/3)(3) \end{pmatrix} = \begin{pmatrix} 1 + 1 \ 2 - 1 \end{pmatrix} = \begin{pmatrix} 2 \ 1 \end{pmatrix}$$

Thus, $x = 2$ and $y = 1$.

Using matrices, solve the system of linear equations: $x + y = 3$ and $2x - y = 3$. - DDCET Q&A

Using matrices, solve the system of linear equations: $x + y = 3$ and $2x - y = 3$.

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