find the product of the following two matrices.\n\nanswer attempt 1 out of 2\nrows: 2 columns: 2

Explanation:

Step1: Calculate the element in the first row and first column

Multiply the elements of the first row of the first matrix by the corresponding elements of the first column of the second matrix and sum them: ((-3)\times(-1)+(-4)\times0 + 1\times0=3)

Step2: Calculate the element in the first row and second column

Multiply the elements of the first row of the first matrix by the corresponding elements of the second column of the second matrix and sum them: ((-3)\times0+(-4)\times1 + 1\times0=-4)

Step3: Calculate the element in the first row and third column

Multiply the elements of the first row of the first matrix by the corresponding elements of the third column of the second matrix and sum them: ((-3)\times(-1)+(-4)\times(-1)+1\times1 = 3 + 4+1=8)

Step4: Calculate the element in the second row and first column

Multiply the elements of the second row of the first matrix by the corresponding elements of the first column of the second matrix and sum them: (5\times(-1)+4\times0 + 3\times0=-5)

Step5: Calculate the element in the second row and second column

Multiply the elements of the second row of the first matrix by the corresponding elements of the second column of the second matrix and sum them: (5\times0+4\times1 + 3\times0=4)

Step6: Calculate the element in the second row and third column

Multiply the elements of the second row of the first matrix by the corresponding elements of the third column of the second matrix and sum them: (5\times(-1)+4\times(-1)+3\times1=-5-4 + 3=-6)

Step7: Calculate the element in the third row and first column

Multiply the elements of the third row of the first matrix by the corresponding elements of the first column of the second matrix and sum them: (4\times(-1)+(-4)\times0+0\times0=-4)

Step8: Calculate the element in the third row and second column

Multiply the elements of the third row of the first matrix by the corresponding elements of the second column of the second matrix and sum them: (4\times0+(-4)\times1+0\times0=-4)

Step9: Calculate the element in the third row and third column

Multiply the elements of the third row of the first matrix by the corresponding elements of the third column of the second matrix and sum them: (4\times(-1)+(-4)\times(-1)+0\times1=-4 + 4+0=0)

Answer:

(\begin{bmatrix}3&-4&8\-5&4&-6\-4&-4&0\end{bmatrix})