Questions: Find the product. [ left[ beginarrayll 1 -7 endarray right] left[ beginarrayrrr 6 -2 4 -1 5 3 endarray right] ]

Solution Steps

To find the product of two matrices, we need to perform matrix multiplication. The first matrix is a 1x2 matrix and the second is a 2x3 matrix. The resulting matrix will be a 1x3 matrix. Each element of the resulting matrix is obtained by taking the dot product of the corresponding row of the first matrix and the column of the second matrix.

We have two matrices: \[ \text{matrix1} = \begin{bmatrix} 1 & -7 \end{bmatrix} \] \[ \text{matrix2} = \begin{bmatrix} 6 & -2 & 4 \\ -1 & 5 & 3 \end{bmatrix} \]

To find the product of these matrices, we calculate each element of the resulting matrix by taking the dot product of the row from the first matrix and the columns from the second matrix.

The resulting matrix is calculated as follows: \[ \text{result} = \begin{bmatrix} 1 \cdot 6 + (-7) \cdot (-1) & 1 \cdot (-2) + (-7) \cdot 5 & 1 \cdot 4 + (-7) \cdot 3 \end{bmatrix} \]

Calculating each element:

1. First element: \( 1 \cdot 6 + (-7) \cdot (-1) = 6 + 7 = 13 \)
2. Second element: \( 1 \cdot (-2) + (-7) \cdot 5 = -2 - 35 = -37 \)
3. Third element: \( 1 \cdot 4 + (-7) \cdot 3 = 4 - 21 = -17 \)

Thus, the resulting matrix is: \[ \text{result} = \begin{bmatrix} 13 & -37 & -17 \end{bmatrix} \]

Final Answer