Now solving x = A * B

Steps to Solve

1. Identify Matrix A and Matrix B

From the given information, we can define Matrix A and Matrix B as follows:

$$ A = \begin{bmatrix} 4 & 2 \ 8 & 5 \ 11 & 9 \end{bmatrix}, \quad B = \begin{bmatrix} -5 & 7 \ -3 & 8 \end{bmatrix} $$

2. Matrix Multiplication Setup

The multiplication ( x = A * B ) will results in a new matrix ( x ). The resulting matrix ( x ) will have dimensions that correspond to the rows of ( A ) and the columns of ( B ). Thus:

$$ x = \begin{bmatrix} r_1 & r_2 \end{bmatrix} $$ Where ( r_1 ) corresponds to the first row and ( r_2 ) corresponds to the second row of ( x ).

3. Perform the Matrix Multiplication

To find the elements of ( x ), we calculate:

$$ x_{ij} = \sum_{k=1}^{n} A_{ik} * B_{kj} $$

Calculating each element:

• First element ( x_{11} ):

$$ x_{11} = (4 \cdot -5) + (2 \cdot -3) = -20 - 6 = -26 $$

• Second element ( x_{12} ):

$$ x_{12} = (4 \cdot 7) + (2 \cdot 8) = 28 + 16 = 44 $$

• Third element ( x_{21} ):

$$ x_{21} = (8 \cdot -5) + (5 \cdot -3) = -40 - 15 = -55 $$

• Fourth element ( x_{22} ):

$$ x_{22} = (8 \cdot 7) + (5 \cdot 8) = 56 + 40 = 96 $$

• Fifth element ( x_{31} ):

$$ x_{31} = (11 \cdot -5) + (9 \cdot -3) = -55 - 27 = -82 $$

• Sixth element ( x_{32} ):

$$ x_{32} = (11 \cdot 7) + (9 \cdot 8) = 77 + 72 = 149 $$

4. Construct the Resulting Matrix

Now that we have all elements, we can construct the resulting matrix ( x ):

$$ x = \begin{bmatrix} -26 & 44 \ -55 & 96 \ -82 & 149 \end{bmatrix} $$