Find the product of the following two matrices

Question

3 -2| 1 -1
0 1| 1 1

Answer 1

To find the product of two matrices, we follow the matrix multiplication rules. Let’s denote the matrices as follows:

Matrix A: $$A=\left(\begin{array}{ccc}3& -20& 1\end{array}\right)$$

Matrix B: $$B=\left(\begin{array}{ccc}1& -11& 1\end{array}\right)$$

The product $C=AB$ is calculated using the formula for matrix multiplication:

$$C_{ij}=\sum _k{A}_{ik}{B}_{kj}$$

Now, we will multiply matrix A by matrix B:

1. Calculate $C_{11}$: $$C_{11}=A_{11}{B}_{11}+A_{12}{B}_{21}=3\cdot 1+(-2)\cdot 1=3-2=1$$

2. Calculate $C_{12}$: $$C_{12}=A_{11}{B}_{12}+A_{12}{B}_{22}=3\cdot (-1)+(-2)\cdot 1=-3-2=-5$$

3. Calculate $C_{21}$: $$C_{21}=A_{21}{B}_{11}+A_{22}{B}_{21}=0\cdot 1+1\cdot 1=0+1=1$$

4. Calculate $C_{22}$: $$C_{22}=A_{21}{B}_{12}+A_{22}{B}_{22}=0\cdot (-1)+1\cdot 1=0+1=1$$

Putting it all together, we have: $$C=\left(\begin{array}{ccc}{C}_{11}& C_{12}{C}_{21}& C_{22}\end{array}\right)=\left(\begin{array}{ccc}1& -51& 1\end{array}\right)$$

Thus, the product of the two matrices is: $$\left(\begin{array}{ccc}1& -51& 1\end{array}\right)$$