1. **State the problem:** We are given the matrix equation $$\begin{pmatrix}4 & 5 \\ 4 & 3\end{pmatrix} \begin{pmatrix}-4 \\ -2\end{pmatrix} = k \begin{pmatrix}26 \\ 22\end{pmatrix}$$ and need to find the scalar value $k$. 2. **Matrix multiplication:** Multiply the 2x2 matrix by the 2x1 matrix on the left side. $$\begin{pmatrix}4 & 5 \\ 4 & 3\end{pmatrix} \begin{pmatrix}-4 \\ -2\end{pmatrix} = \begin{pmatrix}4 \times (-4) + 5 \times (-2) \\ 4 \times (-4) + 3 \times (-2)\end{pmatrix} = \begin{pmatrix}-16 - 10 \\ -16 - 6\end{pmatrix} = \begin{pmatrix}-26 \\ -22\end{pmatrix}$$ 3. **Set up the equation:** The result equals $k$ times the vector $$\begin{pmatrix}26 \\ 22\end{pmatrix}$$ so $$\begin{pmatrix}-26 \\ -22\end{pmatrix} = k \begin{pmatrix}26 \\ 22\end{pmatrix}$$ 4. **Solve for $k$:** Equate components: $$-26 = 26k \implies k = \frac{-26}{26} = -1$$ Check second component: $$-22 = 22k \implies k = \frac{-22}{22} = -1$$ Both components give $k = -1$. 5. **Answer:** The value of $k$ is **-1**.