Given: $$ B=\left[\begin{array}{ll}7 & -3 \ 5 & -1\end{array} ight] \quad C=\left[\begin{array}{cc}1 & -1 \ 13 & -5\end{array} ight] $$ Solve the equation: $$ 2 X+B=C $$ $$ X=[\square $$ $$ \square $$ DONE

Question

Given: $$ B=\left[\begin{array}{ll}7 & -3 \ 5 & -1\end{array}ight] \quad C=\left[\begin{array}{cc}1 & -1 \ 13 & -5\end{array}ight] $$ Solve the equation: $$ 2 X+B=C $$ $$ X=[\square $$ $$ \square $$ DONE

UpStudy AI · Accepted Answer

To solve the equation $$ 2X + B = C $$ for the matrix $$ X $$, follow these steps:

Given:
$$
B = \begin{bmatrix} 7 & -3 \ 5 & -1 \end{bmatrix}, \quad C = \begin{bmatrix} 1 & -1 \ 13 & -5 \end{bmatrix}
$$

1. **Subtract $$ B $$ from both sides:**
$$
2X = C - B
$$

2. **Compute $$ C - B $$:**
$$
C - B = \begin{bmatrix} 1-7 & -1-(-3) \ 13-5 & -5-(-1) \end{bmatrix} = \begin{bmatrix} -6 & 2 \ 8 & -4 \end{bmatrix}
$$

3. **Divide each element by 2 to solve for $$ X $$:**
$$
X = \frac{1}{2}(C - B) = \frac{1}{2} \begin{bmatrix} -6 & 2 \ 8 & -4 \end{bmatrix} = \begin{bmatrix} -3 & 1 \ 4 & -2 \end{bmatrix}
$$

**Final Answer:**
$$
X = \begin{bmatrix} -3 & 1 \ 4 & -2 \end{bmatrix}
$$
$$ X = \begin{bmatrix} -3 & 1 \ 4 & -2 \end{bmatrix} $$

Given:
Solve the equation:

DONE

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