7) [} -5 6 0 ]cdot [3 -1]

To multiply a vector by a matrix, we need to ensure that the dimensions are compatible. The given vector is a 3x1 column vector, and the matrix is a 1x2 row vector. To perform the multiplication, we need to take the dot product of the vector with each column of the matrix.<br /><br />Let's denote the vector as $\mathbf{v} = \begin{bmatrix} -5 \\ 6 \\ 0 \end{bmatrix}$ and the matrix as $\mathbf{M} = \begin{bmatrix} 3 & -1 \end{bmatrix}$.<br /><br />The dot product of $\mathbf{v}$ with the first column of $\mathbf{M}$ is:<br />$(-5) \cdot 3 + 6 \cdot 0 + 0 \cdot (-1) = -15$<br /><br />The dot product of $\mathbf{v}$ with the second column of $\mathbf{M}$ is:<br />$(-5) \cdot (-1) + 6 \cdot 0 + 0 \cdot 3 = 5$<br /><br />Therefore, the result of the multiplication is:<br />$\begin{bmatrix} -15 \\ 5 \end{bmatrix}$<br /><br />So, the final answer is:<br />$\begin{bmatrix} -15 \\ 5 \end{bmatrix}$