Question

find the product of the following two matrices.\\(\begin{bmatrix}-4&-4\\-1&0end{bmatrix}\begin{bmatrix}1&3\\-2&0end{bmatrix}\\)\
answer attempt 1 out of 99

Explanation:

Step1: Calculate first row first column

To find the element in the first row and first column of the product matrix, we multiply the corresponding elements of the first row of the first matrix and the first column of the second matrix and sum them up.
The first row of the first matrix is \([-4, -4]\) and the first column of the second matrix is \(

$$\begin{bmatrix}1\\-2\end{bmatrix}$$

\).
So, \((-4)\times1 + (-4)\times(-2)=-4 + 8 = 4\)

Step2: Calculate first row second column

For the element in the first row and second column, we use the first row of the first matrix and the second column of the second matrix.
The first row of the first matrix is \([-4, -4]\) and the second column of the second matrix is \(

$$\begin{bmatrix}3\\0\end{bmatrix}$$

\).
So, \((-4)\times3+(-4)\times0=-12 + 0=-12\)

Step3: Calculate second row first column

To find the element in the second row and first column, we use the second row of the first matrix and the first column of the second matrix.
The second row of the first matrix is \([-1, 0]\) and the first column of the second matrix is \(

$$\begin{bmatrix}1\\-2\end{bmatrix}$$

\).
So, \((-1)\times1+0\times(-2)=-1 + 0=-1\)

Step4: Calculate second row second column

For the element in the second row and second column, we use the second row of the first matrix and the second column of the second matrix.
The second row of the first matrix is \([-1, 0]\) and the second column of the second matrix is \(

$$\begin{bmatrix}3\\0\end{bmatrix}$$

\).
So, \((-1)\times3+0\times0=-3 + 0=-3\)

Answer:

\(

$$\begin{bmatrix}4&-12\\-1&-3\end{bmatrix}$$

\)