Questions: Find BA. A= [ 4 5 1 5 ] B= [ -1 0 -7 -7 ] BA=

Solution Steps

We are given two matrices \( A \) and \( B \) and are asked to find the product \( BA \). The matrices are:

\[ A = \begin{bmatrix} 4 & 5 \\ 1 & 5 \end{bmatrix}, \quad B = \begin{bmatrix} -1 & 0 \\ -7 & -7 \end{bmatrix} \]

To find \( BA \), we need to multiply matrix \( B \) by matrix \( A \). The product of two matrices \( B \) and \( A \) is calculated by taking the dot product of the rows of \( B \) with the columns of \( A \).

The resulting matrix \( BA \) will be a \( 2 \times 2 \) matrix. We calculate each element as follows:

• The element in the first row, first column of \( BA \) is: \[ (-1) \cdot 4 + 0 \cdot 1 = -4 \]

• The element in the first row, second column of \( BA \) is: \[ (-1) \cdot 5 + 0 \cdot 5 = -5 \]

• The element in the second row, first column of \( BA \) is: \[ (-7) \cdot 4 + (-7) \cdot 1 = -28 - 7 = -35 \]

• The element in the second row, second column of \( BA \) is: \[ (-7) \cdot 5 + (-7) \cdot 5 = -35 - 35 = -70 \]

The resulting matrix \( BA \) is:

\[ BA = \begin{bmatrix} -4 & -5 \\ -35 & -70 \end{bmatrix} \]

Final Answer