Q35. - Algebra 2

Question

For Exercises 34-38, use the figure below.

35. Use matrix multiplication to find BA if $\mathbf{B}\mathbf{=}\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]$

Step-by-Step Solution

Answer

The value ofBA  is:$\mathbf{BA}\mathbf{=}\left[\begin{array}{cccc}0& 8& 4& -4\\ 0& 8& 12& 4\end{array}\right]$

Step 1 ­- Observe the given figure.

The given figure is:

Step 2 ­- Description of step.

It is being given that $B=\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]$

The vertex matrixA is given by: $A=\left[\begin{array}{cccc}0& 4& 2& -2\\ 0& 4& 6& 2\end{array}\right]$

Therefore, the value of BA  is given by:$\begin{array}{c}BA=\left[\begin{array}{cc}2& 0\\ 0& 2\end{array}\right]\cdot \left[\begin{array}{cccc}0& 4& 2& -2\\ 0& 4& 6& 2\end{array}\right]\\ =\left[\begin{array}{cccc}0+0& 8+0& 4+0& -4+0\\ 0+0& 0+8& 0+12& 0+4\end{array}\right]\\ =\left[\begin{array}{cccc}0& 8& 4& -4\\ 0& 8& 12& 4\end{array}\right]\end{array}$

Step 3 ­- Write the value of BA.

The value of BA  is: $BA=\left[\begin{array}{cccc}0& 8& 4& -4\\ 0& 8& 12& 4\end{array}\right]$